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Oseledets Decomposition on Sub semiflows

Marek Kryspin

Abstract

The existence of the Oseledets decomposition on continuously embedded subspaces of Banach spaces is proved in this paper. Natural assumptions facilitating such transfer of the Oseledets decomposition are presented, notably conditions often met by dynamical systems generated by differential equations.

Oseledets Decomposition on Sub semiflows

Abstract

The existence of the Oseledets decomposition on continuously embedded subspaces of Banach spaces is proved in this paper. Natural assumptions facilitating such transfer of the Oseledets decomposition are presented, notably conditions often met by dynamical systems generated by differential equations.
Paper Structure (5 sections, 5 theorems, 52 equations)

This paper contains 5 sections, 5 theorems, 52 equations.

Table of Contents

  1. Preliminaries and definitions
  2. Measurable dynamical systems
  3. Measurable linear skew-product semidynamical systems
  4. Oseledets decomposition
  5. Sub-semiflows

Key Result

Lemma 2.1

For a separable Banach space $X_1$ the mapping $(\mathfrak{B}(\mathcal{L}_{\mathrm{s}}(X_1,X_2))\otimes\mathfrak{B}(X_1), \mathfrak{B}(X_2) )$- measurable.

Theorems & Definitions (13)

  • Definition 1.1: Oseledets decomposition
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Claim 1
  • proof
  • Lemma 2.3
  • proof
  • Theorem 2.1
  • ...and 3 more