CONTINUOUS & DISCONTINUOUS PIECEWISE-SMOOTH ONE-DIMEN MAPS: Invariant Sets and Bifurcation Structures (World Scientific Series on Nonlinear Science, Series A, 95, Band 95) - Hardcover

Buch 14 von 17: World Scientific Series On Nonlinear Science Series A

Avrutin Viktor

 
9789814368827: CONTINUOUS & DISCONTINUOUS PIECEWISE-SMOOTH ONE-DIMEN MAPS: Invariant Sets and Bifurcation Structures (World Scientific Series on Nonlinear Science, Series A, 95, Band 95)
Hardcover
ISBN 10: 9814368822 ISBN 13: 9789814368827
Verlag: World Scientific, 2019

Inhaltsangabe

The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

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Von der hinteren Coverseite

The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

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Verlag
World Scientific
Erscheinungsdatum
2019
Sprache
Englisch
ISBN 10 
9814368822
ISBN 13 
9789814368827
Einband
Gebundene Ausgabe
Anzahl der Seiten
650
Kontakt zum Hersteller
preigu GmbH & Co. KG
mail@preigu.de

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