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Chaos on the interval

The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or ori...

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Autor principal: Ruette, Sylvie
Lenguaje:eng
Publicado: American Mathematical Society 2017
Materias:
Acceso en línea:http://cds.cern.ch/record/2279744
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author Ruette, Sylvie
author_facet Ruette, Sylvie
author_sort Ruette, Sylvie
collection CERN
description The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the "most interesting" part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gives complete proofs and addresses both graduate students and researchers.
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spelling cern-22797442021-04-21T19:05:45Zhttp://cds.cern.ch/record/2279744engRuette, SylvieChaos on the intervalMathematical Physics and MathematicsThe aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the "most interesting" part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gives complete proofs and addresses both graduate students and researchers.American Mathematical Societyoai:cds.cern.ch:22797442017
spellingShingle Mathematical Physics and Mathematics
Ruette, Sylvie
Chaos on the interval
title Chaos on the interval
title_full Chaos on the interval
title_fullStr Chaos on the interval
title_full_unstemmed Chaos on the interval
title_short Chaos on the interval
title_sort chaos on the interval
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2279744
work_keys_str_mv AT ruettesylvie chaosontheinterval