Book Description
This book presents a survey of the field of dynamical systems and its significance for research in complex systems and other fields, based on a careful analysis of specific important examples. It also explains the fundamental underlying mathematical concepts, with a particular focus on invariants of dynamical systems, including a systematic treatment of Morse-Conley theory. Entropy and related concepts in the topological, metric, measure theoretic and smooth settings and some connections with information theory are discussed, and cellular automata and random Boolean networks are presented as specific examples.
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Qualitative Theory of Planar Differential Systems (Universitext)
Freddy Dumortier ,
Jaume Llibre , and
Joan C. Artés
Manufacturer: Springer
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ASIN: 3540328939 |
Book Description
The book deals essentially with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced.
From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.
The book is very appropriate for a first course in dynamical systems. Not only does it provide simple and appropriate proofs, but it also contains a lot of exercises and presents a survey of interesting results with the necessary references to the literature.
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Methods of Qualitative Theory in Nonlinear Dynamics Part 2
Andrey L. Shilnikov ,
Dmitry V. Turaev , and
Leon O. Chua
Manufacturer: World Scientific Publishing Company
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Methods of Qualitative Theory in Nonlinear Dynamics (World Scientific Series on Nonlinear Science, Series a , Part 1)
ASIN: 9810240724 |
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Qualitative Theory of Dynamical Systems (Advanced Series in Dynamical Systems/Vol. 12)
D. J. Luo
Manufacturer: World Scientific Pub Co Inc
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ASIN: 9810212682 |
Book Description
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.
Customer Reviews:
The most hideous of all beasts in the Dungeon of Mechanics.......2001-03-03
I don't know if this book really should be considered a book of Classical Mechanics. The reason is that its first 5 chapters (more than 500 pages!) contain almost all the global analysis you'll ever need to know, plus some quite esoteric topics such as a section on general quantization and infinite-dimensional Hamiltonian systems (with the Schroedinger and Korteweg-deVries equations as examples). Copious figures and reasonably clear notation help the reader to understand the (often hard) topological and geometrical concepts. As a book on analytic mechanics, it seems like killing a cockroach with a bazooka. If you plan to learn MECHANICS with a geometrical flavor, and not GLOBAL ANALYSIS with physical motivations, choose instead the shorter, cleaner and much more inspired book of V. I. Arnold, "Mathematical Methods of Classical Mechanics". If you belong to the second group, it's a good place anyway.
The rest of the book is dedicated to dynamical systems, including a fac-simile of a paper of Kolmogorov. However, the topics could be trated with less fuss (as, for example, in the marvellous little and sadly out-of-print book of David Ruelle).
Immense mathematical maturity required.......2000-09-19
This is a wonderful book. You could loose yourself for almost a whole career here - because this book tries to explain virtually the whole of the subject, right up to all the twentieth century contributions.
Photographs of mathematicians from Gauss and Legendre right up to the most venerable living mathematicians are included in a picture gallery at the front of the book. This is excellent.
The book requires as a beginning, all the material regarding the Hamiltonian and Lagrangian formulations of mechanics - which means you won't have a clue about what the book is saying until you have got somewhat beyond the second year at university. Then the authors start discussing topology, and the ideas which are necessary to re-formulate ideas in quite different clothing. This is very hard - the reader really needs to know about very hard mathematics. Ideas about point set topology are essential because the subject matter encompasses chaotic behaviour and the many body problem. Newtons equations (and this surprises many people) lead to large systems of non-linear equations - and the general theory of the solution of such systems leads almost inevitably to poincare point sets, winding numbers, and so forth. The theory of integral operators (see Kranoselsky, et al) has long been couched in these terms.
Get this by all means, and prepare to have a hard journey ahead.
I should mention that many parts of the book are quite readable and the authors go out of their way to reach the reader as far as possible.
It's actually a physically large book, it would be probably better to get the hard back edition if it's available.
Foundations of Mechanics- An absolute must.......2000-07-14
Along with a handful of other works this book is a must for anyone interested in geometric mechanics and control. The text provides a rigorous foundation for a huge subject.
All necessary background is self-contained. However, the book is difficult and I would not recommend it as a first learning text. For that I would send you to Frankel's _The Geometry of Physics_.
Product Description
We introduce a geometric mechanism for diffusion in a priori unstable nearly integrable dynamical systems. It is based on the observation that resonances, besides destroying the primary KAM tori, create secondary tori and tori of lower dimension. We argue that these objects created by resonances can be incorporated in transition chains taking the place of the destroyed primary KAM tori. We establish rigorously the existence of this mechanism in a simple model that has been studied before. The main technique is to develop a toolkit to study, in a unified way, tori of different topologies and their invariant manifolds, their intersections as well as shadowing properties of these bi-asymptotic orbits. This toolkit is based on extending and unifying standard techniques. A new tool used here is the scattering map of normally hyperbolic invariant manifolds. The model considered is a one-parameter family, which for $\varepsilon = 0$ is an integrable system. We give a small number of explicit conditions the jet of order $3$ of the family that, if verified imply diffusion. The conditions are just that some explicitely constructed functionals do not vanish identically or have non-degenerate critical points, etc. An attractive feature of the mechanism is that the transition chains are shorter in the places where the heuristic intuition and numerical experimentation suggests that the diffusion is strongest.
Book Description
This book is an introduction to the qualitative theory of dynamical systems on manifolds of low dimension (on the circle and on surfaces). Along with classical results, it reflects the most significant achievements in this area obtained in recent times by Russian and foreign mathematicians whose work has not yet appeared in the monographic literature. The main stress here is put on global problems in the qualitative theory of flows on surfaces.
Despite the fact that flows on surfaces have the same local structure as flows on the plane, they have many global properties intrinsic to multidimensional systems. This is connected mainly with the existence of nontrivial recurrent trajectories for such flows. The investigation of dynamical systems on surfaces is therefore a natural stage in the transition to multidimensional dynamical systems.
The reader of this book need be familiar only with basic courses in differential equations and smooth manifolds. All the main definitions and concepts required for understanding the contents are given in the text.
The results expounded can be used for investigating mathematical models of mechanical, physical, and other systems (billiards in polygons, the dynamics of a spinning top with nonholonomic constraints, the structure of liquid crystals, etc.).
In our opinion the book should be useful not only to mathematicians in all areas, but also to specialists with a mathematical background who are studying dynamical processes: mechanical engineers, physicists, biologists, and so on.
Customer Reviews:
Va-Voom!.......2007-07-05
I'd always been curious about this one, ever since the scene in the film The Impossible Years where the younger sister's eyes pop (along with her bubble gum bubble) as she reads it.
All I can say is, if you're looking for beautifully written erotica that stands up to the test of time (read: It'll turn on even us 21st century, uncensored folks), this is for you. Enjoy!
Realistic Morality.......2006-02-13
In this time of erotic fiction galore, where novels of sexual content line bookstore shelves, and purchasing one is as easy, common place, and unembarassing as picking up a bar of chocolate at a grocery store, the true significance of Fanny Hill may not be quite fully understood. The story documents a young girl's experiences following the untimely death of her parents, which leaves her in an adult situation at a tender age. Penniless and alone, she strives to locate a means of survival for one in her position, unexperienced in the world. Not surprisingly, and as the title proclaims, she becomes a woman of pleasure.
What is surprising, however, is the morality of the characters, how Cleland emphasizes their humanity and conscience, how he illustrates that their profession has no baring on their propensity for evil, provides no leniencey for a souless disposition. Cleland continuosly establishes this point throught the course of the novel, explaining, through Fanny, that courteseans and the like are regular people. That they work, eat, and play, just like everyone else. This is not necesssarly the main point of the novel, merely an important observation to remember with regards to the period the work was written. This perspective, in addition to the erotic material, must have clashed with the traditional, conservative beliefs of the time, been considered blasphemy. The author must have realized this, and knowing this fact while reading the material makes me have a bit more respect for the writer.
As for the rest, the memoir is privy to an extensive English vocabulary, and the choppy, comma-spliced sentences maintain a unique elegance in contrast with the regular style of uninform diction.
All in all, I found it a really stellar work, and picking it up I had pretty low expectations considering the basic story line, which serves as the framework for so many novels today. I actually wound up reading the entire work in one sitting, and finding it an enticing blend of romance and intrigue, action and realistic adventure, advancing the ideals of morality from a mature and logical standpoint.
Book Description
Fanny Hill, shrouded in controversy for most of its more than 250-year life, and banned from publication in the United States until 1966, was once considered immoral and without literary merit, even earning its author a jail sentence for obscenity.
The tale of a naïve young prostitute in bawdy eighteenth-century London who slowly rises to respectability, the novel–and its popularity–endured many bannings and critics, and today
Fanny Hill is considered an important piece of political parody and sexual philosophy on par with French libertine novels.
This uncensored version is set from the 1749 edition and includes commentary by Charles Rembar, the lawyer who defended the novel in the 1966 U.S. Supreme Court case, and newly commissioned notes.
Customer Reviews:
give it a read--but just once.......2006-01-27
Maybe it's because I don't think it's particularly newsworthy that people in the 18th century had sex (after all there wouldn't have been people the 19th, 20th, or 21st centuries, otherwise, and lots of the other 18th century novels and quite a few of the poems give the secret away). And I'm not saying, "Don't read Fanny Hill," because it is an interesting read once, as interesting to read as any 18th century tale that's purely about sex would be. But it's not high literary art--while entertaining to read once, it's really little more than a picaresque sex tale, clearly designed for men to read, moving from one incident to another with a "reforming" ending tacked on. The plot setup is totally unrealistic and perfunctory--i mean, would any woman in any century ever write down her sexual activity in such detail to send to another woman to read as memoirs?? As a novel, it pales in comparison to any of the other myriad 18th century works that feature sex as a plot element (e.g., Defoe's Moll Flanders, Fielding's Tom Jones, Matthew Lewis's The Monk, de Laclos' Les Liaisons Dangereuses, and so forth). The difference between those works and this one isn't just the explicitness, it's the fact that in those other works the sex serves a purpose in a larger plot. They may not get into the size of their characters' "machines" but they're simply better, more entertaining books over the long haul. So I'd say check this one out from your public library (it's all right, no one will suspect its contents!) and spend your money to feast on Tom Jones and his late night "conversations" instead.
ENJOYABLE READ ON SEVERAL LEVELS.......2005-06-16
I have always been rather fond of this work. Not only is it well written, in a Victorian way, but it is a very nice "dirty book" to boot. There is never really anything crass or gross in the book, the author's use of the language sees to that. The story is certainly realistic, there is humor and a certain sadness all at one time. I am old enough to be able to remember when this particular work was not available in the United States. Thank goodness those days are over. We did miss a lot of purely good writing in those days. I am not at all sure if this one is appropriate for a High School Lit. class, but is certainly worth the read and the study for the more mature reader. On the other hand, the work is certainly a lot less graphic than some of the material the kids have ready access at any time. All in all I have to recommend this one. It is interesting and certainly gives us a good lesson in writing.
It's all about sex..........2004-05-18
...Even if it seems like it isn't, it really is. Let's face it, the critics and scholars have tried to dignify the reading and "study" of this text to make the dirty pleasure more dignified. THis is almost like the guys who claim to only look at Playboy for the articles, and not the articles of clothing. It's amusing when professors assign this book, usually the new young male ones.;)
A worthy classic.......2003-07-11
This book is fascinating, not merely as an erotic novel (and the historical significance of this book cannot be denied) but also as a glimpse of society and mores of the mid-18th century.
Fanny is an orphaned girl who goes to London to Seek Her Fortune and ends up with a career alternating between prostitution and being a kept woman. Unlike most porn, she's not always happy about her sexual encounters, and there are times when she's heartbroken over a lost love. She's decieved by a woman who claims to be hiring her "as a companion," in a another scene she's exploited by a money-hungry landlord.
As she grows older, though, Fanny becomes more in charge of her sexuality and more open to exploration. We, as readers, also see a glimpse of 18th-century prostitution and the demimonde of kept mistresses (which many wealthy men of the period kept).
Hardly a rollicking farce (there are times when sex has serious consequences) but at times it is humorous. Never crass or vulgar, but nevertheless explicit, this bawdy gem is worth checking out. Fanny is always honest about herself and what she does to survive, and pulls no punches. (I took away a star because, at times, it is difficult going because of the outdated language, but don't let that deter you.)
Pleasurable and delightful.......2002-07-23
This little book amazed me the first time I read it, for it is a delightful mix of erotica and story-telling in olde English. Sensuality with style and elegance, without being vulgar or hackneyed, or boring. With an excellent portrayal of the title character, this book deals in detail a very sexual theme, taking you to a different time. Shows how love, passion, and pleasure survive every age and time. Delightful.
Product Description
Memoirs of a Woman of Pleasure, better known as Fanny Hill, is one of the most notorious texts in English literature. As recently as 1963 an unexpurgated edition was the subject of a trial, yet in the eighteenth century John Cleland's open celebration of sexual enjoyment was a best selling novel. Fanny's story, as she falls into prostitution and then rises to respectability, takes the form of a confession that is vividly coloured by copious and explicit physiological details of her carnal adventures. The moral outrage that this has always provoked has only recently been countered by serious critical appraisal.
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Fanny Hill, Or Memoirs Of A Woman Of Pleasure
John Cleland
Manufacturer: Olympiapress.com
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Binding: Paperback
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ASIN: 1596540427 |
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A notorious classic. Fanny Hill was first published by Cleland in 1749. The subject of immediate controversy (and an arrest), it lingered through the ages in an expurgated form. This version, first published by the Olympia Press in 1956 as Memoirs of Fanny Hill, contains the complete, unexpurgated edition.
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Fanny Hill or Memoirs of a Woman of Pleasure
John Cleland
Manufacturer: Adamant Media Corporation
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Binding: Paperback
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ASIN: 0543903788
Release Date: 2000-05-06 |
Book Description
John Cleland (1710-1789) - an English writer, journalist and translator. His novel"Fanny Hill, or Memories of a Woman of Pleasure" is an erotic masterpiece, which narratesabout scandalous events taking place in the life of a woman, her disreputable adventures.The views on life of eighteenth century bourgeoisie combined with sexual passion and romantic love.
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Fanny Hill: Memoirs of a Woman of Pleasure
John Cleland
Manufacturer: Dell Publishing Company
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Binding: Paperback
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ASIN: 0440055555 |
Customer Reviews:
Surprisingly modern, contemporary illustrations, .......2006-12-07
Surprisingly explicit book, John Cleland's book has been well illustrated with contemporary paintings, cartoons and sketches, such as Thomas Rowland, Hogarth and Francois Boucher
Fanny Hill is a clandestine classic, richly erotic, it tells the story of a young girl from the country who is drawn into the teeming underwold of eighteenth century London.
Always good-humoured Fanny makes the best of her fate and the story of her rise through harlotry to reiches and respectability is told with vigour and wit
John Cleland manages to bring Fanny Hill's London to life. Vivid and amusing and highly spiced, it is an entertinaing and readble - even at times romantic account.
It is surprisingly modern in its text. The interesting subtext to this is the surprising nature of its explicitness, quite unexpected for that age. The book, I think, has survived so long because it has a very sympathetic development of the character of Fanny, and despite being racy she has some depth of feeling. The language is also fairly easy reading, not steeped too far in the archaic.
Product Description
Mass market paperback by Signet (NAL), 1965, 222 pp. Introduction by noted historian/author J. H. Plumb. Classic erotica that has remained alive despite bannings, burnings, and constant suppression. The pleasures of the flesh without a a flicker of guilt.
Product Description
A history of the life of a harlot, a bawdy house girl in eighteenth century London. Complete with photos by Bronzino, Chaplin, Coubet, Amaury-Duval, Gervex, Rembrant, and others.
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