Moduli for heteroclinic connections involving saddle-foci and periodic solutions

Alexandre A. P. Rodrigues

doi:10.3934/dcds.2015.35.3155

Article Contents

2015, Volume 35, Issue 7: 3155-3182. Doi: 10.3934/dcds.2015.35.3155

This issue Previous Article Variational analysis of semilinear plate equation with free boundary conditions Next Article Multi-peak positive solutions for a fractional nonlinear elliptic equation

Moduli for heteroclinic connections involving saddle-foci and periodic solutions

Alexandre A. P. Rodrigues^1,

1.
Centro de Matemática da Universidade do Porto and Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto

Received: March 2014

Revised: December 2014

Published: May 2017

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Abstract

Dimension three is the lowest dimension where we can find chaotic behaviour for flows and it may be helpful to distinguish in advance ``equivalent'' complex dynamics. In this article, we give numerical invariants for the topological equivalence of vector fields on three-dimensional manifolds whose flows exhibit one-dimensional heteroclinic connections involving either saddle-foci or periodic solutions. Computed as an infinite limit time, these moduli of topological equivalence heavily rely on the behaviour near the invariant saddles. We also present an alternative proof of the Togawa's Theorem.

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Mathematics Subject Classification: Primary: 37C15; Secondary: 37C20, 37C27, 37C29, 37C70.

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