by Albert D Morozov (Nizhny Novgorod State University, Russia) , Timothy N Dragunov (Nizhny Novgorod State University, Russia) , Svetlana A Boykova (Nizhny Novgorod State University, Russia) , & Olga V Malysheva (Nizhny Novgorod State University, Russia)

Table of Contents (115k)
Preface (58k)
Chapter 1: Introduction (1,372k)

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.

• Computer-Generated Invariant Sets:
  • Description of WInSet Program
  • List of the Built-in Equations, Maps and Fractals of WInSet. Main Invariant Sets of WInSet
• Mathematical Description of Invariant Sets:
  • Invariant Sets in Hamiltonian Mechanics
  • Area-Preserving Maps
  • Non-Conservative Systems
  • Non-Conservative Maps
  • Diffusion Equations