Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures
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A01=Fabio Tramontana
A01=Iryna Sushko
A01=Laura Gardini
A01=Viktor Avrutin
Author_Fabio Tramontana
Author_Iryna Sushko
Author_Laura Gardini
Author_Viktor Avrutin
Border Collision Bifurcations
Category=PBWR
Crisis Bifurcations
Degenerate Bifurcations
Discontinuous Maps
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Homoclinic Bifurcations
Map Replacement Technique
One-Dimensional Maps
Period Adding
Period Incrementing
Piecewise-Linear Maps
Piecewise-Smooth Maps
Robust Chaos
Skew Tent Map
Product details
- ISBN 9789814368827
- Publication Date: 14 Jun 2019
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
