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Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics (Cambridge Studies in Advanced Mathematics)

*- Paperback*

ISBN: 0521475724

[SR: 6078296], Paperback, [EAN: 9780521475723], Cambridge University Press, Cambridge University Press, Book, [PU: Cambridge University Press], Cambridge University Press, This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits, and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including Hénon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic sets turn out to play an important role in determining which class of dynamics is prevalent near a bifurcation. The authors provide a new, more geometric proof of Newhouse's theorem on the co-existence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics., 13911, Differential Equations, 226699, Applied, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 226700, Geometry & Topology, 13928, Algebraic Geometry, 13930, Analytic Geometry, 13932, Differential Geometry, 13936, Non-Euclidean Geometries, 13987, Topology, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13917, Fractals, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 491546, Geometry, 468218, Mathematics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics (Cambridge Studies in Advanced Mathematics)

*- Paperback*

ISBN: 0521475724

[SR: 6078296], Paperback, [EAN: 9780521475723], Cambridge University Press, Cambridge University Press, Book, [PU: Cambridge University Press], Cambridge University Press, This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits, and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including Hénon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic sets turn out to play an important role in determining which class of dynamics is prevalent near a bifurcation. The authors provide a new, more geometric proof of Newhouse's theorem on the co-existence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics., 13911, Differential Equations, 226699, Applied, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 226700, Geometry & Topology, 13928, Algebraic Geometry, 13930, Analytic Geometry, 13932, Differential Geometry, 13936, Non-Euclidean Geometries, 13987, Topology, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13917, Fractals, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 491546, Geometry, 468218, Mathematics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dyna

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ISBN: 9780521475723

ID: 1755413

This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits, and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including Henon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic sets turn out to play an important role in determining which class of dynamics is prevalent near a bifurcation. The authors provide a new, more geometric proof of Newhouse's theorem on the co-existence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics. Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics Palis, J. / Palis, Jacob / Takens, Floris, Cambridge University Press

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Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations : Fractal Dimensions and Infinitely Many Attractors in Dynamics

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ISBN: 0521475724

ID: 15463167

This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits, and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including Henon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic sets turn out to play an important role in determining which class of dynamics is prevalent near a bifurcation. The authors provide a new, more geometric proof of Newhouse's theorem on the co-existence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics. math,mathematics,science and math Mathematics, Cambridge University Press

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** Details of the book - Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics**

EAN (ISBN-13): 9780521475723

ISBN (ISBN-10): 0521475724

Paperback

Publishing year: 1995

Publisher: CAMBRIDGE UNIV PR

248 Pages

Weight: 0,381 kg

Language: eng/Englisch

Book in our database since 05.05.2007 18:53:53

Book found last time on 28.12.2017 00:38:09

ISBN/EAN: 0521475724

ISBN - alternate spelling:

0-521-47572-4, 978-0-521-47572-3

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