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About this product
- DescriptionIn 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 t quite hyperbolic. However, they possess eugh 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.
- Author(s)K.J. Palmer
- PublisherSpringer-Verlag New York Inc.
- Date of Publication09/12/2010
- Series TitleMathematics and its Applications
- Series Part/Volume Number501
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Note1 black & white illustrations, biography
- Weight486 g
- Width156 mm
- Height234 mm
- Spine16 mm
- Format DetailsTrade paperback (US)
- Edition Statement1st ed. Softcover of orig. ed. 2000
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