Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures (Hardcover)

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.

General

Imprint:	World Scientific Publishing Co Pte Ltd
Country of origin:	Singapore
Series:	World Scientific Series on Nonlinear Science Series A, 95
Release date:	June 2019
First published:	June 2012
Authors:	Viktor Avrutin • Laura Gardini • Iryna Sushko • Fabio Tramontana
Dimensions:	160 x 236 x 42mm (L x W x T)
Format:	Hardcover
Pages:	648
ISBN-13:	978-981-4368-82-7
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science
LSN:	981-4368-82-2
Barcode:	9789814368827

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