Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds: Classical and Quantum Aspects (Mathematics and Its Applications)

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This book is unique in providing a detailed exposition of modern Lie-algebraic theory of integrable nonlinear dynamic systems on manifolds and its applications to mathematical physics, classical mechanics and hydrodynamics. The authors have developed a canonical geometric approach based on differential geometric considerations and spectral theory, which offers solutions to many quantization procedure problems. Much of the material is devoted to treating integrable systems via the gradient-holonomic approach devised by the authors, which can be very effectively applied. Audience: This volume is recommended for graduate-level students, researchers and mathematical physicists whose work involves differential geometry, ordinary differential equations, manifolds and cell complexes, topological groups and Lie groups.

Algebraic Integrability, Painlevé Geometry and Lie Algebras (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)

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Algebraic Integrability, Painlevé Geometry and Lie Algebras (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
Mark Adler , Pierre van Moerbeke , and Pol Vanhaecke
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 354022470X

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This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.

Differential Geometry of Foliations: The Fundamental Integrability Problem (Springer Series in Wood Science)

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Differential Geometry of Foliations: The Fundamental Integrability Problem (Springer Series in Wood Science)
Bruce L. Reinhart
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

Geometry and Integrability (London Mathematical Society Lecture Note Series)

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Geometry and Integrability (London Mathematical Society Lecture Note Series)

Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521529999

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Based on courses held at the Feza GÜrsey Institute, this collection of survey articles introduces advanced graduate students to an exciting area on the border of mathematics and mathematical physics. Including articles by key names such as Calogero, Donagi and Mason, it features the algebro-geometric material from Donagi as well as the twistor space methods in Woodhouse's contribution, forming a bridge between the pure mathematics and the more physical approaches.

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This collection of survey articles is based on a semester held at the Feza Gürsey Institute to introduce advanced graduate students to this exciting area lying on the border of mathematics and mathematical physics. There are articles by some key names such as Calogero, Donagi and Mason himself. One attractive feature is the inclusion of the algebro-geometric material from Donagi as well as the twistor space methods exemplified by Woodhouse's article, which forms a bridge between the pure mathematics and the more physical approaches. This book should provide an excellent resource for graduate students wishing to move on to research.

Geometry, Integrability & Quantization (Proceedings of the Sixth International Conference)

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Geometry, Integrability & Quantization (Proceedings of the Sixth International Conference)

Manufacturer: Natl Museum of Bulgaria
ProductGroup: Book
Binding: Paperback

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ASIN: 9548495295

Integrability and Nonintegrability in Geometry and Mechanics (Mathematics and its Applications)

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Integrability and Nonintegrability in Geometry and Mechanics (Mathematics and its Applications)
A.T. Fomenko
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 9027728186

The integrability problem for G-structures

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The integrability problem for G-structures
V Guillemin
Manufacturer: Columbia University Dept. of Mathematics
ProductGroup: Book
Binding: Unknown Binding
ASIN: B0007FFZ62

Integrability, Self-Duality, and Twistor Theory (London Mathematical Society Monographs New Series)

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Integrability, Self-Duality, and Twistor Theory (London Mathematical Society Monographs New Series)
L. Mason , and N. M. J. Woodhouse
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0198534981

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It has been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection (for example, the Korteweg-de Vries and nonlinear Schr"odinger equations are reductions of the self-dual Yang-Mills equation). This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and second that twistor theory provides a uniform geometric framework for the study of B"acklund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them.

Geometry, Integrability & Quantization, Proceedings of the 8th International Conference

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Geometry, Integrability & Quantization, Proceedings of the 8th International Conference

Manufacturer: Coronet Books Inc
ProductGroup: Book
Binding: Paperback

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Translated and with an Introduction by Joachim Neugroschel"Death in Venice" is about a ruinous quest for love and beauty. Gustave von Aschenbach, a successful but lonely author, travels to Venice in search of elusive fulfillment. There he is spellbound by a beautiful Polish boy and finds himself fettered to this hypnotic city of eerie physical decay and sun-drenched sensuality. Renowned for his translations of Franz Kafka and Joseph Roth, Joachim Neugroschel places the true emphasis on Mann's mythic fascination with sexual inhibition and the havoc it wreaks--elements that were downplayed in earlier translations of his fiction. Capturing his evocative and bewitching style as well as his mordant irony, this new translation is the definitive English-language version of Mann's most famous tales and novellas, many of them still controversial today. The collection includes "The Will for Happiness," "Little Herr Friedemann," "Tobias Mindernickel," "Little Lizzy," "Gladius Dei," "Tristan," "The Starvelings," "Tonio Kroger," "The Wunderkind," "Harsh Hour," and "The Blood of the Walsungs."

Customer Reviews:

Classic Tale.......2006-02-23

Since I first read this book as a Comparative Literature major at the University of Washington, Thomas Mann has been right up there with Balzac, Strindberg, and Joyce as one of the best Modern writers.

different translation.......2004-10-13

These stories are all very fine. However, I found this translation lacking some kind of esthetic satisfaction that I always get from an earlier translation of Mann's work by Helen T. Porter.

Perfectly Executed.......2003-08-13

I don't think that Death in Venice operates on the premise that a "life of sensation" is worthwhile, whatever the cost. Mann's story is a complication of the traditional morality tale, and Aschenbach's demise is not a result of his giving in to the pursuit of beauty and visceral experience, but of his previous, total rejection of this kind of surrender. Aschenbach, we are told, lives like a "closed fist," and for this reason is completely unequipped to deal with the combined experience of visiting an unfamiliar and sinister place, and of encountering a boy who provokes a strong physical and emotional response (on a sidenote, occasionally I hear someone label this as a homophobic text, but they are entirely missing the point, I think. As in Henry James's Daisy Miller, Death in Venice, on one level, illustrates the way that forces outside of sex can make sex, or the desire for sex, fatal. It has nothing to do with the act, or desire, itself). It is Aschenbach's perpetual need to take the proverbial "high road" that makes his foray into the world of the sensual so disastrous.
The story is brilliant. Not only does Mann address wonderful themes like the nature of art, artistic impulse, desire, repression, and Orientalism, even, but the writing and narrative trajectory are flawless.

Great stories with profound meaning, but a little unsettling.......2003-02-11

Thomas Mann was one of the most elegant writers of our century. His prose dances off the page with a fluidity that is all too rare in today's world of literature, and his narrative style is always compelling. This little volume is a collection of twelve short stories. For the most part, the stories are enjoyable, though a couple of them are downright disturbing. Many of them feature dejected and misunderstood people who are desperately struggling to be understood and accepted in the world, and a great deal of the main characters are artists.

But there is much more here than just stories. In fact, nearly all these tales contain deep and complicated questions. What is art? What constitutes legitimate art? Is it true that true art brings pain, and that true artists can never live or enjoy life? These and many other questions are considered throughout this work.

As I said, some of these stories are a bit disturbing, and a couple are downright creepy. I recommend proceeding with caution. It might even be best to start with one of Mann's novels (like Buddenbrooks, for example). Still, if you are willing to brave this one out, it promises to be a richly rewarding experience, both in its quality of narrative and in the message that each of these short tales is meant to convey.

reading death in venice as an artist.......2002-12-12

Death in Venice is one of the gratest and most intelectually stimulating books i have ever read. It gives an example of the impoartance of beauty to the human soul. Without beauty there is no reason to live but in the deep lust for beauty the subject is consumed and dies. It askes the question is life without beauty worth living especially if life without beauty is only half a life. Death in Venice is one of the only books, along with The Picture of Dorian Gray by Oscar Wilde, that recognises this idea and shows us that a life of sensation may not be so wrong even if it may ultimately costs life but what is life without beauty. It is the subject of all artists as Keats said "beauty is truth and truth beauty" Byron's life of excess caused his exile and what stands on the lips of literary history are the words "all art is immoral" spoken by Oscar Wilde who's entire life was for beauty. Death in Venice is in proud tradition of the celebration of beauty even if beauty is a cause of destrucion.

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Death in Venice and Other Tales
Thomas Mann
Manufacturer: Penguin Classics
ProductGroup: Book
Binding: Paperback
ASIN: B000OJHMCG

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Regret Comes From Lack of Self-Awareness
Gorgeous
Poetic Pedophilia
Excellent Translation in Dover Edition - Helpful Commentary
Zero stars if I could

Death in Venice and Other Tales
Thomas Mann
Manufacturer: Amereon Limited
ProductGroup: Book
Binding: Hardcover

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ASIN: 0848805747

Book Description

Celebrated novella of a middle-aged German writer's tormented passion for a Polish youth met on holiday in Venice, and its tragic consequences. Powerful evocation of the mysterious forces of death and disintegration in the midst of existence, and the isolation of the artist in 20th-century life. New translation and extensive commentary.

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Regret Comes From Lack of Self-Awareness.......2006-08-26

Thomas Mann has taken an ages old theme, the attraction of an older, worn out man for a youthful boy, dressed it up in a series of classical allusions, and details how this attraction merely accelerates the decay of the man whose decline began long before he first saw the boy. In DEATH IN VENICE, Gustave von Aschenbach is a German writer living in pre-World War I Europe, who has been trying to balance the struggles involved in maintaining his hard-worn writing laurels with the demands those struggles have placed on his life, his health, and his emotional keel. He has become an ascetic, denying himself the pleasures of the flesh. His muse is a jealous one and demands his attention full time. Over the years, he has willingly paid the price, but the true cost becomes apparent to him only as he turns fifty years of age. He senses a void in his life. He does not know what it is or how to compensate, so he decides that travel in the answer. One of the ironies of Mann's novella is that Aschenbach's readers undoubtedly give him credit for the worldly-wise sophisticate that his many literary works of art suggest he must be. But the truth is that because of his rigorous denial of himself, in terms of maturity and emotional serenity, he is a greenhorn. He tends to view the world as he does through his books, which are laden with an abundance of classical erudition. But the real world is not Plato's Republic reborn. It is a testing ground which favors those whose feet are firmly grounded in the world of the body. Early on, as Mann subtly alludes to Aschenbach's mental and physical infirmities, his fate is a doom foretold.

Aschenbach is puzzled by the continual appearance of a weird looking old man who pops up at convenient moments to glare at him in a puzzling manner. The first time that Aschenbach sees him, he pays him scant attention, but as the visits increase in his trips around Europe, both Aschenbach's and the reader's wonderment grow. After a while, the old man begins to assume allegorical--or at least mystical--proportions. One can almost see a misty haze envelop both during their encounters. It is tempting to treat these visitations as unreal hallucinations of a mind slowly unhinging with Aschenbach seeing a version of himself, following him around Europe, as if to remind him of his looming mortality.

While in Europe, he notices a good looking Polish boy of about fourteen. Aschenbach begins to fantasize about him but dares not do more than just gaze at him from a distance. As if in a rush, the years of ascetic self-denial rupture, opening the door to his latent homosexual tendencies. Mann cleverly avoids calling a spade a spade. Instead he dresses up this fantasy in terms of Aschenbach's limited social background that had been fueled by a lifetime of classical learning. The boy, whose name is Tadziu, is described as a young Adonis, an Apollo, and other such. The only words that pass between then occur at the very end, when Aschenbach sees the boy tormented by bullies and almost, but not quite, intervenes. Aschenbach locks eyes with the boy and in that moment he knows the forbidden joy that, in a different universe might have been his. He dies, possibly of the plague, happy and decidedly ignorant of who he himself really was. Mann passes no moral judgments against Aschenbach. This is no gay bashing novel nor does he hold it up as a trumpeting to engage in illicit activities, but in the ending of what-might-have-been, Mann suggests that life's choices and future happiness might better be served with a clearer moral vision of who we are, what we want, and where we are going.

Gorgeous.......2006-08-20

Mann's masterpiece is an achingly beautiful, exquisitely crafted, spellbinding exploration of beauty, age, love, sex, life, and of course death. I can think of no other book where the setting so effectively establishes the book's atmosphere, so powerfully reinforces its themes and ideas. The plot is so simple, yet wrapped in layers of meaning, both inviting and resisting interpretation.

This book is short yet incredibly rich; it reminds me of a tiny, delicately carved precious jewel. And what a beautiful jewel to dive into and immerse oneself in. Read this book!

Poetic Pedophilia .......2005-11-13

I did not like this book as much as many of the other reviewers. The main problem I had was that I simply could not relate to Aschenbach, the protaganist of the story. I mean, I thought that his obsession with the male child was weird. Unlike Lolita, there was no dark humor in the obsession. There was just a very raw, profound, longing and appreciation for the beauty of the young child. I found that somewhat sick and I cannot say that I've ever had many of the feelings that Aschenbach relates in the work.

Many people seem to think that the most boring part of this book is the part where Aschenbach thinks about his art. Maybe I'm an odd duck, but I actually found this to be the most interesting part of the novella. I like how Aschenbach talks about how he wants to make a name for himself through his art, and about how he wakes up early every morning to pour his soul into his craft. This is the part of the book that I best understood. It really resonated with me.

Even though the story was not my favorite, I must say that I appreciated the author's use of language. The translation I read (by Stanley Applebaum) was lively and captured the author's verbal imagination. I will probably never read this novella again, but I do think that I might like other work by Mann (provided that he is writing about different subject matter!).

I do not know who would really appreciate this book. I guess I would recommend this book largely to people who appreciate art for art's sake, and also to people who like novels which really penetrate the psyche of the main character. Readers less artistically inclined might find this work to be heavy sledding.

Excellent Translation in Dover Edition - Helpful Commentary .......2005-05-30

Death in Venice (1912) is a disturbing story, one that is not easy to forget. It is also exceptional literature, a classic of the twentieth century. Thomas Mann's Death in Venice might be best compared to the subtle, psychologically complex fiction of Henry James, Joseph Conrad, and Fyodor Dostoevsky.

In Munich the aging, highly respected author Gustav Aschenbach is in need of change, rest in a new setting, to overcome his growing fatigue that is impacting his writing. While recovering in Venice, Aschenbach slowly, but inexorably, becomes mesmerized by a young Polish boy staying at the seashore with his aristocratic family. Aschenbach is intellectually aware of his growing obsession, but he is seemingly unable to break away. Thomas Mann's somber portrayal of this troubled man is a masterpiece of subtle nuances and psychological intensity.

Thomas Mann's lengthy sentences and complex grammatical structures severely complicate the task of translating Death in Venice. I have read two excellent and yet substantially different translations. The most faithful translation is by Stanley Appelbaum (in this Dover edition, 1995) that tries to be as literal as possible, carefully preserving the comparative length of the original sentences as well as the internal sequence of each original German sentence. Contrastingly, the H. T. Lowe-Porter translation (found elsewhere) is less literal, but is considered the most delightful and readable version, although at the expense of subdividing many of Mann's lengthy sentences. Lowe-Porter's version has been the standard translation for many years.

The Dover edition provides an excellent 10-page commentary, including footnotes.

Zero stars if I could.......2005-01-09

I was a philosophy major in college and I hated this book. But then again, the whole NAMBLA fic genre really doesn't do it for me. I'm sure some literary aesthetes are going to pick this review apart, good for them. I'm incredibly well-read and thought this one was just a tepid bore. Save your time, read some Dostoevsky, some Dickens, some Milton, (...).

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Death in Venice and Other Tales

Manufacturer: Recorded Books Inc
ProductGroup: Book
Binding: Audio Cassette
ASIN: 0788724827

Product Description

Featuring his world-famous masterpiece, "Death in Venice," this new collection of Nobel laureate Thomas Mann's stories and novellas reveals his artistic evolution. In this new, widely acclaimed translation that restores the controversial passages that were cut out of the original English version, "Death in Venice" tells about a ruinous quest for love and beauty amid degenerating splendor. Gustav von Aschenbach, a successful but lonely author, travels to the Queen of the Adriatic in search of an elusive spiritual fulfillment that turns into his erotic doom. Spellbound by a beautiful Polish boy, he finds himself fettered to this hypnotic city of sun-drenched sensuality and eerie physical decay. Also included in this volume are eleven other stories by Mann: "Tonio Kroger," "Gladius Dei," "The Blood of the Walsungs," "The Will for Happiness," "Little Herr Friedmann," "Tobias Mindernickel," "Little Lizzy," "Tristan," "The Starvelings," "The Wunderkind," and "Harsh Hour." All of the stories collected here display Mann's inimitable use of irony, his subtle characterizations, and superb, complex plots.

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