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Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures by Viktor Avrutin (Univ Of Stuttgart, Germany) at Abbey's Bookshop,
Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures...
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Viktor Avrutin (Univ Of Stuttgart, Germany) Laura Gardini (Univ Of Urbino, Italy)

Continuous And Discontinuous Piecewise-smooth One-dimensional Maps

Invariant Sets And Bifurcation Structures

Viktor Avrutin (Univ Of Stuttgart, Germany),  Laura Gardini (Univ Of Urbino, Italy),  Iryna Sushko (National Academy Of Sciences, Ukraine & Kyiv School Of Economics, Ukraine) ,  Fabio Tramontana (Catholic Univ Of Milan, Italy)

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English
World Scientific Publishing Co Pte Ltd
29 May 2019
Non-linear science
Series: 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.
By:   , , , , , , ,
Imprint:   World Scientific Publishing Co Pte Ltd
Country of Publication:   Singapore
Volume:   95
ISBN:   9789814368827
ISBN 10:   9814368822
Series:   World Scientific Series on Nonlinear Science Series A
Pages:   648
Publication Date:  
Audience:   College/higher education ,  Further / Higher Education
Format:   Hardback
Publisher's Status:   Active
Introduction: Continuous and Discontinuous Piecewise-Smooth and Especially Piecewise-Linear Models (An Overview). Bifurcations in Piecewise Smooth Systems; General Concepts: Border Collision and Crisis Bifurcations, Map Replacement Technique; Continuous Piecewise-Linear Maps: Bifurcation Structures in Regular and Chaotic Domains; Discontinuous Piecewise-Linear Maps: Period Adding and Bandcount Adding Bifurcation Structures; Discontinuous Piecewise-Linear Maps: Period Increment and Bandcount Increment Bifurcation Structures; Multi-Dimensional Parameter Spaces and Their Organizing Centers.

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