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Softcover ISBN:  9781470429560 
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Softcover ISBN:  9781470429560 
Product Code:  ULECT/67 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470437596 
Product Code:  ULECT/67.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9781470429560 
eBook ISBN:  9781470437596 
Product Code:  ULECT/67.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 67; 2017; 215 ppMSC: Primary 37
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 higherdimensional 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 LiYorke 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.
To see a diagram of the relations between the main notions studied in this book, click on “Read more”.
ReadershipGraduate students and researchers interested in onedimensional dynamical systems.

Table of Contents

Chapters

Notation and basic tools

Links between transitivity, mixing and sensitivity

Periodic points

Topological entropy

Chaos in the sense of LiYorke, scrambled sets

Other notions related to LiYorke pairs: Generic and dense chaos, distributional chaos

Chaotic subsystems

Appendix: Some background in topology


Additional Material

Reviews

[W]hile successfully presenting an updated account of a very lively area of mathematical research, the book is selfcontained (only skipping full proofs when some extensions of the results to graph maps are discussed) and accessible even to graduate students, which is quite remarkable...this is a most welcome addition to the corpus in this field.
Victor Jiménez Lépez, Mathematical Reviews


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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 higherdimensional 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 LiYorke 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.
To see a diagram of the relations between the main notions studied in this book, click on “Read more”.
Graduate students and researchers interested in onedimensional dynamical systems.

Chapters

Notation and basic tools

Links between transitivity, mixing and sensitivity

Periodic points

Topological entropy

Chaos in the sense of LiYorke, scrambled sets

Other notions related to LiYorke pairs: Generic and dense chaos, distributional chaos

Chaotic subsystems

Appendix: Some background in topology

[W]hile successfully presenting an updated account of a very lively area of mathematical research, the book is selfcontained (only skipping full proofs when some extensions of the results to graph maps are discussed) and accessible even to graduate students, which is quite remarkable...this is a most welcome addition to the corpus in this field.
Victor Jiménez Lépez, Mathematical Reviews