Cell-to-cell mapping: a method of global analysis for nonlinear systems / C. S. Hsu

Auteur: Hsu, Chieh Su (1922-2014) - AuteurType de document: Livre numériqueCollection: Applied mathematical sciences ; 64Langue: anglaisÉditeur: Berlin : Springer, 1987 ISBN: 0387965203 Note: This monograph is an introduction to the methods of cell-to-cell mappings and their application to the study of global behavior of (both deterministic and stochastic) nonlinear systems. The leading idea of these methods is to divide the (continuum) state space into cells and study the corresponding cell-to-cell mappings. These methods are computer-oriented and make it possible to obtain concrete results for highly nonlinear systems (location of attractors and domains of attraction, determination of their statistical properties etc.). The theory of cell-to-cell mappings has been (and still is being) developed by the present author and his collaborators; there are many open problems to be solved by pure mathematicians, numerical analysts and computer scientists. (Zentralblatt) Sujets MSC: 58-02 Global analysis, analysis on manifolds -- Research exposition (monographs, survey articles)
37C70 Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Attractors and repellers, topological structure
54H20 General topology -- Connections with other structures, applications -- Topological dynamics
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This monograph is an introduction to the methods of cell-to-cell mappings and their application to the study of global behavior of (both deterministic and stochastic) nonlinear systems. The leading idea of these methods is to divide the (continuum) state space into cells and study the corresponding cell-to-cell mappings. These methods are computer-oriented and make it possible to obtain concrete results for highly nonlinear systems (location of attractors and domains of attraction, determination of their statistical properties etc.). The theory of cell-to-cell mappings has been (and still is being) developed by the present author and his collaborators; there are many open problems to be solved by pure mathematicians, numerical analysts and computer scientists. (Zentralblatt)

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