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Infinite-Dimensional Dynamical Systems in Mechanics and Physics

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Cover of 'Infinite-Dimensional Dynamical Systems in Mechanics and Physics'

Table of Contents

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    Book Overview
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    Chapter 1 General Introduction. The User’s Guide
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    Chapter 2 General Results and Concepts on Invariant Sets and Attractors
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    Chapter 3 Elements of Functional Analysis
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    Chapter 4 Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction—Diffusion Equations. Fluid Mechanics and Pattern Formation Equations
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    Chapter 5 Attractors of Dissipative Wave Equations
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    Chapter 6 Lyapunov Exponents and Dimension of Attractors
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    Chapter 7 Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems
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    Chapter 8 Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions
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    Chapter 9 The Cone and Squeezing Properties. Inertial Manifolds
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    Chapter 10 Inertial Manifolds and Slow Manifolds. The Non-self-adjoint Case
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    Chapter 11 Approximation of Attractors and Inertial Manifolds. Convergent Families of Approximate Inertial Manifolds
Attention for Chapter 7: Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems
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