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Dynamics of Topologically Generic Homeomorphisms (Memoirs of the American Mathematical Society)

*- Paperback*

2003, ISBN: 9780821833384

ID: 319261198

American Mathematical Society, 2003-07-01. Paperback. New. Brand new. We distribute directly for the publisher. The goal of this work is to describe the dynamics of generic homeomorphisms of certain compact metric spaces $X$. Here "generic" is used in the topological sense -- a property of homeomorphisms on $X$ is generic if the set of homeomorphisms with the property contains a residual subset (in the sense of Baire category) of the space of all homeomorphisms on $X$. The spaces $X$ we consider are those with enough local homogeneity to allow certain localized perturbations of homeomorphisms; for example, any compact manifold is such a space. We show that the dynamics of a generic homeomorphism is quite complicated, with a number of distinct dynamical behaviors coexisting (some resemble subshifts of finite type, others, which we call `generalized adding machines', appear strictly periodic when viewed to any finite precision, but are not actually periodic). Such a homeomorphism has infinitely many, intricately nested attractors and repellors, and uncountably many distinct dynamically-connected components of the chain recurrent set. We single out several types of these "chain components", and show that each type occurs densely (in an appropriate sense) in the chain recurrent set. We also identify one type that occurs generically in the chain recurrent set. We also show that, at least for $X$ a manifold, the chain recurrent set of a generic homeomorphism is a Cantor set, so its complement is open and dense. Somewhat surprisingly, there is a residual subset of $X$ consisting of points whose limit sets are chain components of a type other than the type of chain components that are residual in the space of all chain components. In fact, for each generic homeomorphism on $X$ there is a residual subset of points of $X$ satisfying a stability condition stronger than Lyapunov stability., American Mathematical Society, 2003-07-01

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Dynamics of Topologically Generic Homeomorphisms (Memoirs of the American Mathematical Society)

*- Paperback*

2003, ISBN: 0821833383

ID: 2717383365

[EAN: 9780821833384], Neubuch, [PU: American Mathematical Society], Science|General, Brand new. We distribute directly for the publisher. The goal of this work is to describe the dynamics of generic homeomorphisms of certain compact metric spaces $X$. Here "generic" is used in the topological sense -- a property of homeomorphisms on $X$ is generic if the set of homeomorphisms with the property contains a residual subset (in the sense of Baire category) of the space of all homeomorphisms on $X$. The spaces $X$ we consider are those with enough local homogeneity to allow certain localized perturbations of homeomorphisms; for example, any compact manifold is such a space. We show that the dynamics of a generic homeomorphism is quite complicated, with a number of distinct dynamical behaviors coexisting (some resemble subshifts of finite type, others, which we call `generalized adding machines', appear strictly periodic when viewed to any finite precision, but are not actually periodic). Such a homeomorphism has infinitely many, intricately nested attractors and repellors, and uncountably many distinct dynamically-connected components of the chain recurrent set. We single out several types of these "chain components", and show that each type occurs densely (in an appropriate sense) in the chain recurrent set. We also identify one type that occurs generically in the chain recurrent set. We also show that, at least for $X$ a manifold, the chain recurrent set of a generic homeomorphism is a Cantor set, so its complement is open and dense. Somewhat surprisingly, there is a residual subset of $X$ consisting of points whose limit sets are chain components of a type other than the type of chain components that are residual in the space of all chain components. In fact, for each generic homeomorphism on $X$ there is a residual subset of points of $X$ satisfying a stability condition stronger than Lyapunov stability.

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ISBN: 0821833383

ID: 2221769838

[EAN: 9780821833384], Neubuch, [PU: American Mathematical Society], BRAND NEW, Dynamics of Topologically Generic Homeomorphisms, Ethan Akin, Mike Hurley, Judy A. Kennedy, The goal of this work is to describe the dynamics of generic homeomorphisms of certain compact metric spaces $X$. Here 'generic' is used in the topological sense - a property of homeomorphisms on $X$ is generic if the set of homeomorphisms with the property contains a residual subset (in the sense of Baire category) of the space of all homeomorphisms on $X$. The spaces $X$ we consider are those with enough local homogeneity to allow certain localized perturbations of homeomorphisms; for example, any compact manifold is such a space. We show that the dynamics of a generic homeomorphism is quite complicated, with a number of distinct dynamical behaviors coexisting (some resemble subshifts of finite type, others, which we call 'generalized adding machines', appear strictly periodic when viewed to any finite precision, but are not actually periodic).Such a homeomorphism has infinitely many, intricately nested attractors and repellors, and uncountably many distinct dynamically-connected components of the chain recurrent set. We single out several types of these 'chain components', and show that each type occurs densely (in an appropriate sense) in the chain recurrent set. We also identify one type that occurs generically in the chain recurrent set. We also show that, at least for $X$ a manifold, the chain recurrent set of a generic homeomorphism is a Cantor set, so its complement is open and dense. Somewhat surprisingly, there is a residual subset of $X$ consisting of points whose limit sets are chain components of a type other than the type of chain components that are residual in the space of all chain components. In fact, for each generic homeomorphism on $X$ there is a residual subset of points of $X$ satisfying a stability condition stronger than Lyapunov stability.

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Dynamics of Topologically Generic Homeomorphisms (Memoirs of the American Mathematical Society)

*- Paperback*

2014, ISBN: 9780821833384

ID: 809013478

American Mathematical Society, 2014. Paperback. New Book. Paperback. Dooley and Zhang extend the notion of continuous bundle random dynamical system to the setting where the action of group R or group N is replaced by the action of an infinite countable discrete amenable group. Given such a system and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theory entropy. They also discuss some variants of this variational principle. They introduce both topological and measure-theory entropy tuples for continuous bundle random dynamical systems, and use their variational principles to obtain a relationship between these entropy tuples. (2014 Ringgold, Inc., Portland, OR), American Mathematical Society, 2014, Amer Mathematical Society. PAPERBACK. 0821833383 **NEW** Factory Sealed. Book is in excellent condition. No remainder marks. Shipped with delivery confirmation inside US. *g MM2-31 . New., Amer Mathematical Society

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** Details of the book - Dynamics of Topologically Generic Homeomorphisms (Memoirs of the American Mathematical Society)**

EAN (ISBN-13): 9780821833384

ISBN (ISBN-10): 0821833383

Paperback

Publishing year: 2003

Publisher: Amer Mathematical Society

Book in our database since 07.05.2007 08:18:06

Book found last time on 28.08.2017 00:32:04

ISBN/EAN: 0821833383

ISBN - alternate spelling:

0-8218-3338-3, 978-0-8218-3338-4

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