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Dynamical systems with hyperbolic behavior

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Published by Springer-Verlag in Berlin, New York .
Written in English


  • Differentiable dynamical systems,
  • Hyperbolic spaces,
  • Chaotic behavior in systems

Book details:

Edition Notes

StatementD.V. Anosov (ed.).
SeriesEncyclopaedia of mathematical sciences ;, v. 66, Dynamical systems ;, 9, Dinamicheskie sistemy., 9.
ContributionsAnosov, D. V.
LC ClassificationsQA805 .D5613 1988 vol. 9, QA614.8 .D5613 1988 vol. 9
The Physical Object
Paginationp. cm.
ID Numbers
Open LibraryOL1120802M
ISBN 103540570438, 0387570438
LC Control Number94047311

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Get this from a library! Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour. [D V Anosov] -- The book deals with smooth dynamical systems with hyperbolic behaviour of trajectories filling out "large subsets" of the phase space. Such systems . Dynamical systems / 9 Dynamical systems with hyperbolic behaviour. Author: Vladimir I Arnold ; Jakov G Sinaj ; Dmitrij V Anosov ; Valerij V Kozlov ; Revaz V Gamkrelidze ; All authors. Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Stephen Wiggins. Springer Science & Business Media, - Mathematics - pages. 1 Reviews: 1. About this Textbook In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds.

Uniformly hyperbolic systems are now fairly well understood. They may exhibit very complex behavior which, nevertheless,admits a very precise description. Moreover, uniform hyperbolicity is the main ingredient for characterizing structural stability of a dynamicalsystem. Buy Dynamical Systems IX: Dynamical Systems with Hyperbolic Behaviour (Encyclopaedia of Mathematical Sciences) Softcover reprint of hardcover 1st ed. by D. V. Anosov (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.   The existence of invariant measures for smooth dynamical systems follows in the next chapter with a good introduction to Lagrangian mechanics. Part 2 of the book is a rigorous overview of hyperbolicity with a very insightful discussion of stable and unstable s: 6. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions.

Glossary Definition Introduction Linear Systems Local Theory Hyperbolic Behavior: Viana M. () Hyperbolic Dynamical Systems. In: Meyers R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY Search book. Search within book. Type for suggestions. Table of contents Previous. 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. It presents hyperbolic systems of first-order partial differential equations in the canonic forms of Courant-Lax and of Schauder. For these systems in a slab Da = [0 ≥ x ≥ a, y ɛ E r] of the xy-space E r+1, the chapter presents the formulation of certain boundary value problems, and presents the corresponding theorems of existence of the. The theory of uniformly hyperbolic dynamical systems was initiated in the 's (though its roots stretch far back into the 19th century) by S. Smale, his students and collaborators, in the west.