Chaos on the Interval
Seiten
2017
American Mathematical Society (Verlag)
978-1-4704-2956-0 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2956-0 (ISBN)
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Surveys the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. Some of the more recent developments in the field, 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 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.
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.
Sylvie Ruette, Universite Paris-Sud, Orsay, France.
Notation and basic tools
Links between transitivity, mixing and sensitivity
Periodic points
Topological entropy
Chaos in the sense of Li-Yorke, scrambled sets
Other notions related to Li-Yorke pairs: Generic and dense chaos, distributional chaos
Chaotic subsystems
Appendix: Some background in topology
Bibliography
Notation
Index
| Erscheinungsdatum | 29.03.2017 |
|---|---|
| Reihe/Serie | University Lecture Series |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 408 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-2956-X / 147042956X |
| ISBN-13 | 978-1-4704-2956-0 / 9781470429560 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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