Continuous & Discontinuous Piecewise-Smooth One-Dimen Maps
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Book Overview The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applicati...
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.
Book Details Format: Hardcover | Pages: 634 | Language: English | Publisher: WORLD SCIENTIFIC PUB CO INC | ISBN: 9814368822
FormatHardcover
Pages634
LanguageEnglish
ISBN9814368822
EAN9789814368827
PublisherWORLD SCIENTIFIC PUB CO INC
Publication Date1970-01-01
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight2.27 Pounds
Length9.0 Inches
Width6.0 Inches
Height1.38 Inches
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