ScholarLens Back to search
1986•Proceedings of the Royal Society of Edinburgh Section A MathematicsRequires access

Bifurcation from a homoclinic orbit in parabolic differential equations

C. Miguel Blázquez

Open publisher page 16 citations

Abstract

Synopsis This paper considers autonomous parabolic equations which have a homoclinic orbit to an isolated equilibrium point. We study these systems under autonomous perturbations. Firstly we prove that the perturbation under which the homoclinicorbit persists forms a submanifold of codimension one. Then, if a perturbation of this manifold is considered, we prove that a unique stable periodic orbit arises from the homoclinic orbit under certain conditions for the eigenvalues of thesaddle point.

About this research paper

What this paper is about

Synopsis This paper considers autonomous parabolic equations which have a homoclinic orbit to an isolated equilibrium point. We study these systems under autonomous perturbations. Firstly we prove that the perturbation under which the homoclinicorbit persists forms a submanifold of codimension one. Then, if a perturbation of this manifold is considered, we prove that a unique stable periodic orbit arises from the homoclinic orbit under certain conditions for the eigenvalues of thesaddle point.

Why it matters

OpenAlex reports 16 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Synopsis This paper considers autonomous parabolic equations which have a homoclinic orbit to an isolated equilibrium point. We study these systems under autonomous perturbations. Firstly we prove that the perturbation under which the homoclinicorbit persists forms a submanifold of codimension one. Then, if a perturbation of this manifold is considered, we prove that a unique stable periodic orbit arises from the homoclinic orbit under certain conditions for the eigenvalues of thesaddle point.

Key concepts: Homoclinic orbit, Homoclinic bifurcation, Heteroclinic orbit, Submanifold, Perturbation (astronomy), Mathematical analysis, Codimension, Mathematics

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
Bifurcation from a homoclinic orbit in parabolic differential equations — Research Paper | ScholarLens