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Chaos on the Interval

Von:

Ruette, Sylvie, 1975- [aut]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: University Lecture Series ; v.67Verlag: Providence : American Mathematical Society, 2017Beschreibung: 1 Online-Ressource (231 p)Schlagwörter:

Andere physische Formen: 1470437597 | 9781470437596 | 147042956X. | 9781470429560. | Erscheint auch als: Chaos on the interval. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2017. xii, 215 Seiten | Print version: Chaos on the Interval. Providence : American Mathematical Society,c2017MSC: MSC: *37-02 | 37E05 | 37B40 | 54H20RVK: RVK: SK 810 | SI 165LOC-Klassifikation:

QA297.75.R84 2017

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Zusammenfassung: 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 chZusammenfassung: 5.3. Positive entropy maps are Li-Yorke chaotic5.4. Zero entropy maps; 5.5. One Li-Yorke pair implies chaos in the sense of Li-Yorke; 5.6. Topological sequence entropy; 5.7. Examples of maps of type 2^{∞}, Li-Yorke chaotic or not; Chapter 6. Other notions related to Li-Yorke pairs: Generic and dense chaos, distributional chaos; 6.1. Generic and dense chaos; 6.2. Distributional chaos; Chapter 7. Chaotic subsystems; 7.1. Subsystems chaotic in the sense of Devaney; 7.2. Topologically mixing subsystems; 7.3. Transitive sensitive subsystems; Chapter 8. Appendix: Some background in topologyZusammenfassung: 5.3. Positive entropy maps are Li-Yorke chaotic5.4. Zero entropy maps; 5.5. One Li-Yorke pair implies chaos in the sense of Li-Yorke; 5.6. Topological sequence entropy; 5.7. Examples of maps of type 2^{∞}, Li-Yorke chaotic or not; Chapter 6. Other notions related to Li-Yorke pairs: Generic and dense chaos, distributional chaos; 6.1. Generic and dense chaos; 6.2. Distributional chaos; Chapter 7. Chaotic subsystems; 7.1. Subsystems chaotic in the sense of Devaney; 7.2. Topologically mixing subsystems; 7.3. Transitive sensitive subsystems; Chapter 8. Appendix: Some background in topologyZusammenfassung: Cover; Title page; Contents; Preface; Contents of the book; Chapter 1. Notation and basic tools; 1.1. General notation; 1.2. Topological dynamical systems, orbits, -limit sets; 1.3. Intervals, interval maps; 1.4. Chains of intervals and periodic points; 1.5. Directed graphs; Chapter 2. Links between transitivity, mixing and sensitivity; 2.1. Transitivity and mixing; 2.2. Accessible endpoints and mixing; 2.3. Sensitivity to initial conditions; Chapter 3. Periodic points; 3.1. Specification; 3.2. Periodic points and transitivity; 3.3. Sharkovsky's Theorem, Sharkovsky's order and typeZusammenfassung: 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 chPPN: PPN: 897974050Package identifier: Produktsigel: ZDB-4-NLEBK

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