Continuous and Discontinuous Piecewise-Smooth One-Dimensional Maps: Invariant Sets and Bifurcation Structures
Language: English
Published by WSPC, 2019
Series: Book 14 of 17 - World Scientific Series On Nonlinear Science Series A
- Hardcover
- New
Seller: moluna, Greven, Germanymoluna
AbeBooks seller since July 9, 2020
Condition: New
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Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Focuses on both continuous and discontinuous one-dimensional piecewise-linear maps and summarizes the results related to bifurcation structures in regular and robust chaotic domains.InhaltsverzeichnisIntroduction: Continuous and Disc.
Seller Inventory # 256904187
- Title
- Continuous and Discontinuous Piecewise-Smooth One-Dimensional Maps: Invariant Sets and Bifurcation Structures
- Author
- Iryna Sushko|Laura Gardini|Viktor Avrutin
- Publisher
- WSPC
- Publication year
- 2019
- Condition
- New
- Binding
- Gebunden
- Language
- English
- ISBN 10
- 9814368822
- ISBN 13
- 9789814368827
- Series
- Book 14 of 17: World Scientific Series On Nonlinear Science Series A
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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