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Invariance Principle and dynamics

François Ledrappier

Abstract

This is a survey of some invariances that arise in dynamical systems theory in the presence of zero Lyapunov exponents.

Invariance Principle and dynamics

Abstract

This is a survey of some invariances that arise in dynamical systems theory in the presence of zero Lyapunov exponents.
Paper Structure (35 sections, 48 theorems, 118 equations)

This paper contains 35 sections, 48 theorems, 118 equations.

Table of Contents

  1. Introduction
  2. Examples of applications of an invariance principle
  3. Product of independent $2\times2$ matrices. Exponents. Furstenberg criterion
  4. Application to discrete 1-d Schrödinger equation.
  5. Random homeomorphisms in dimension 1
  6. Compact extension of hyperbolic systems
  7. Invariance Principle
  8. Basic setting
  9. Proof of theorem \ref{['IP']}
  10. Remarks and complements
  11. Non-ergodic case
  12. Regularity
  13. Perturbations
  14. Deformations
  15. Comments
  16. ...and 20 more sections

Key Result

Theorem 2.1

There is a number $\gamma \ge 0$ such that, for $\overline m$-a.e. $x \in \overline X,$

Theorems & Definitions (88)

  • Theorem 2.1: FK60
  • Theorem 2.2: Furstenberg F63
  • proof
  • Definition 2.3
  • Proposition 2.4
  • proof
  • Proposition 2.5: Basic inequality
  • proof
  • Corollary 2.6
  • Theorem 2.7: I73
  • ...and 78 more