Fixed points, bounded orbits and attractors of planar flows

TL;DR

This paper characterizes isolated invariant continua as global attractors in planar dissipative flows and provides conditions under which such continua are attractors or repellers.

Contribution

It offers a dynamical characterization of invariant continua as attractors and establishes criteria distinguishing attractors from repellers in planar flows.

Findings

Provides a characterization of isolated invariant continua as global attractors.

Derives a sufficient condition for an invariant continuum to be an attractor or repeller.

Enhances understanding of the structure of planar dissipative flows.

Abstract

In this paper we provide a dynamical characterization of isolated invariant continua which are global attractors for planar dissipative flows. As a consequence, a sufficient condition for an isolated invariant continuum to be either an attractor or a repeller is derived for general planar flows.