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Field name	Details
Dewey Class	515.352
Title	Shadowing in Dynamical Systems ([EBook]) : Theory and Applications / by Ken Palmer.
Author	Palmer, Kenneth James , 1945-
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Springer US , 2000.
Physical Details	XIV, 300 pages : online resource.
Series	Mathematics and its applications ; 501
ISBN	9781475732108
Summary Note	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.:
Contents note	1 Hyperbolic Fixed Points of Diffeomorphisms and Their Stable and Unstable Manifolds -- 2 Hyperbolic Sets of Diffeomorphisms -- 3 Transversal Homoclinic Points of Diffeomorphisms and Hyperbolic Sets -- 4 The Shadowing Theorem for Hyperbolic Sets of Diffeomorphisms -- 5 Symbolic Dynamics Near a Transversal Homoclinic Point of a Diffeomorphism -- 6 Hyperbolic Periodic Orbits of Ordinary Differential Equations, Stable and Unstable Manifolds and Asymptotic Phase -- 7 Hyperbolic Sets of Ordinary Differential Equations -- 8 Transversal Homoclinic Points and Hyperbolic Sets in Differential Equations -- 9 Shadowing Theorems for Hyperbolic Sets of Differential Equations -- 10 Symbolic Dynamics Near a Transversal Homoclinic Orbit of a System of Ordinary Differential Equations -- 11 Numerical Shadowing -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4757-3210-8
Links to Related Works	Subject References: Differential equation . Differential equations — Numerical solutions . Electronic data processing . Numeric Computing . Numerical Analysis . Ordinary differential equations . Shadowing (Differentiable dynamical systems) . Authors: Palmer, Kenneth James 1945- . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications . Classification: 515.352 .

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Shadowing in Dynamical Systems: Theory and Applications

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