Chapter 1 General Introduction. The User’s Guide

Chapter 2 General Results and Concepts on Invariant Sets and Attractors

Chapter 3 Elements of Functional Analysis

Chapter 4 Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction—Diffusion Equations. Fluid Mechanics and Pattern Formation Equations

Chapter 5 Attractors of Dissipative Wave Equations

Chapter 6 Lyapunov Exponents and Dimension of Attractors

Chapter 7 Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems

Chapter 8 Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions

Chapter 9 The Cone and Squeezing Properties. Inertial Manifolds

Chapter 10 Inertial Manifolds and Slow Manifolds. The Non-self-adjoint Case