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Shadowing in Dynamical Systems
By:K.J. Palmer
Published on 2000-02-29 by Springer Science & Business Media

In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.

This Book was ranked at 19 by Google Books for keyword Classical dichotomy.

Book ID of Shadowing in Dynamical Systems's Books is OcD9oXqmmW0C, Book which was written byK.J. Palmerhave ETAG "PbBE0r+QYZ8"

Book which was published by Springer Science & Business Media since 2000-02-29 have ISBNs, ISBN 13 Code is 9780792361794 and ISBN 10 Code is 0792361792

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Book which have "300 Pages" is Printed at BOOK under CategoryMathematics

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