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Some questions concerning attractors for non-autonomous dynamical systems

Russell Johnson, Víctor Muñoz-Villarragut

Abstract

We compare various concepts of attractor in the context of non-autonomous dynamical systems. Then, we prove an appropriate version of the Pliss reduction principle for non-autonomous differential systems with rapidly oscillating coefficients.

Some questions concerning attractors for non-autonomous dynamical systems

Abstract

We compare various concepts of attractor in the context of non-autonomous dynamical systems. Then, we prove an appropriate version of the Pliss reduction principle for non-autonomous differential systems with rapidly oscillating coefficients.
Paper Structure (3 sections, 11 theorems, 57 equations)

This paper contains 3 sections, 11 theorems, 57 equations.

Table of Contents

  1. Introduction
  2. Attractors
  3. Asymptotic phase and reduction principle

Key Result

Proposition 2.3

Let $A\subset\mathfrak P\times\mathbb R^d$ be a compact invariant set. Then $A$ is a Lyapunov attractor if and only if it is a pullback attractor.

Theorems & Definitions (19)

  • Definition 2.1
  • Definition 2.2
  • Proposition 2.3
  • proof
  • Proposition 2.4
  • proof
  • Definition 3.2
  • Theorem 3.3
  • Theorem 3.4
  • Proposition 3.5: fajp
  • ...and 9 more