Overview

This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical systems to computer design.In Part II, the invariant sets presented in Part I are investigated from the theoretical perspective. The invariant sets of dynamical systems with one, one-and-a-half and two degrees of freedom, as well as those of two-dimensional maps, are discussed. The basic models of the diffusion equations are also considered. This part of the book is intended for a more advanced reader, with at least a BSc in Mathematics.Contents: Computer-Generated Invariant Sets: Description of WInSet ProgramList of the Built-in Equations, Maps and Fractals of WInSet. Main Invariant Sets of WInSet Mathematical Description of Invariant Sets: Invariant Sets in Hamiltonian MechanicsArea-Preserving MapsNon-Conservative SystemsNon-Conservative MapsDiffusion EquationsReadership: Mathematicians, physicists and engineers.

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9781299615212

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