| Introduction | p. 1 |
| Invariant Structures Everywhere | p. 1 |
| Resonance Structures in Celestial Mechanics | p. 2 |
| Cellular, Spiral, Vortex and Crystal Structures | p. 4 |
| Fractals | p. 9 |
| Dynamical Systems | p. 11 |
| Attractors | p. 13 |
| Invariant Tori | p. 15 |
| Discrete Dynamical Systems--Maps | p. 16 |
| Computer-Generated Invariant Sets | p. 19 |
| Description of WInSet Program | p. 21 |
| Installation | p. 21 |
| Basics of WInSet | p. 21 |
| First Run of WInSet | p. 22 |
| Using the Mouse and the Keyboard | p. 23 |
| Your First Invariant Set | p. 24 |
| WInSet Menu | p. 25 |
| Three-Dimensional Objects | p. 35 |
| Diffusion Equations | p. 36 |
| Defining Your Own Equations | p. 41 |
| List of the Built-in Equations, Maps and Fractals of WInSet. Main Invariant Sets of WInSet | p. 45 |
| Maps | p. 45 |
| Cathala Map | p. 45 |
| Chirikov Map | p. 45 |
| Henon Maps | p. 47 |
| Julia Map | p. 47 |
| Mira and Gumowski Maps | p. 48 |
| Zaslavsky Map | p. 52 |
| Fractals | p. 52 |
| Coloring the Fractals | p. 52 |
| Julia Fractals | p. 53 |
| Mandelbrot Fractal | p. 56 |
| Mira Fractals | p. 56 |
| Newton Fractal | p. 57 |
| Ordinary Differential Equations (ODE) | p. 57 |
| Brusselator | p. 57 |
| Chua Equations | p. 58 |
| Duffing Type Equations | p. 58 |
| Hamiltonian Systems on Torus | p. 62 |
| Henon-Heiles Model | p. 62 |
| Henon-Heiles Type Equations | p. 63 |
| Kepler Equation | p. 63 |
| Kolmogorov-Volterra Equations | p. 63 |
| Lorenz Equations | p. 65 |
| Motion of Particle in Gravitation Field | p. 65 |
| Pendulum Equations | p. 67 |
| Equations with Quadratic Nonlinearity | p. 69 |
| Roessler Equations | p. 70 |
| Volterra Equations | p. 70 |
| Diffusion Equations (PDE) | p. 71 |
| Brusselator Model | p. 71 |
| Fitz Hugh-Nagumo Equations | p. 72 |
| Lengyel-Epstein Model (CIMA) | p. 72 |
| Semi-Discrete Equation | p. 73 |
| Numerical Methods Used by WInSet | p. 74 |
| Mathematical Description of Invariant Sets | p. 77 |
| Invariant Sets in Hamiltonian Mechanics | p. 79 |
| Generalities | p. 79 |
| Invariant Sets of Hamiltonian Systems with One Degree of Freedom | p. 82 |
| Invariant Sets of Hamiltonian Systems with 3/2 Degrees of Freedom | p. 90 |
| Poincare Map | p. 90 |
| Analytic Study | p. 93 |
| Duffing Type Equations | p. 98 |
| Pendulum Type Equation | p. 101 |
| Systems on the Torus | p. 104 |
| Kepler Equation | p. 104 |
| Invariant Sets of Hamiltonian Systems with Two Degrees of Freedom | p. 106 |
| Henon-Heiles Type Systems | p. 106 |
| Invariant Sets in the Dynamics of a Solid | p. 107 |
| Area-Preserving Maps | p. 111 |
| Chirikov Map | p. 111 |
| Gumowski and Mira Map | p. 113 |
| Henon Map | p. 113 |
| Zaslavsky Map | p. 118 |
| Non-Conservative Systems | p. 123 |
| Characteristics of Chaotic Dynamics | p. 124 |
| Characteristics which do not Use Measure | p. 125 |
| Measure-Theoretic Characteristics of the Attractor | p. 127 |
| Power Spectrum of an Observable | p. 129 |
| Self-Oscillations | p. 130 |
| Some Technical Transformations | p. 132 |
| Qualitative Behavior of Solutions in an Individual Cell | p. 134 |
| Behavior of Solutions near Separatrices of the Unperturbed System | p. 136 |
| Van der Pole-Duffing Type Equations | p. 137 |
| Pendulum Type Equations | p. 138 |
| Brusselator Equation | p. 140 |
| Three-Dimensional Systems | p. 143 |
| Resonances and Synchronization | p. 145 |
| Theoretical Analysis of Quasi-Hamiltonian Systems with 3/2 Degrees of Freedom | p. 146 |
| Characteristics of Chaotic Dynamics for Systems with 3/2 Degrees of Freedom | p. 160 |
| Theoretical Analysis of Quasi-Hamiltonian Systems with Two Degrees of Freedom | p. 162 |
| Examples | p. 169 |
| Parametric Resonances | p. 177 |
| General Results | p. 178 |
| Example 1 | p. 186 |
| Example 2 | p. 190 |
| Strange Attractors in Three-Dimensional Systems | p. 198 |
| Lorenz System | p. 198 |
| Roessler System | p. 205 |
| Chua System | p. 205 |
| Non-Conservative Maps | p. 211 |
| One-Dimensional Maps | p. 213 |
| Two-Dimensional Non-Conservative Maps | p. 216 |
| One-Dimensional Complex Rational Endomorphisms | p. 216 |
| Fractals | p. 219 |
| Non-Invertible Mira Maps and their Fractals | p. 226 |
| Henon Map | p. 232 |
| Diffusion Equations | p. 235 |
| Parabolic Equations | p. 236 |
| One-Component Models | p. 236 |
| Two-Component Model | p. 238 |
| Semi-Discrete Approximation | p. 243 |
| Approximation of Equation (8.1) | p. 244 |
| Approximation of the Basic Multi-Component Models | p. 245 |
| Semi-Discrete Diffusion Equations | p. 245 |
| Bibliography | p. 251 |
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