Work

Topology of attractors and periodic points

Year: 2024

Type: article

Abstract: The dynamics of a dissipative and area contracting planar homeomorphism were described in terms of the attractor. This was a subset of the plane defined as the maximal compact invariant set. We proved that the coexistence of two fixed points and an $ N $-cycle produced some topological complexity: the attractor cannot be arcwise connected. The proofs were based on the theory of prime ends.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2024083

Authors: Rafael Ortega, Alfonso Ruiz-Herrera

Institution: Universidad de Granada

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Ministerio de Ciencia e Innovación

Award: G7152046867