Tokyo Journal of Mathematics

Hopf-homoclinic Bifurcations and Heterodimensional Cycles

Shuntaro TOMIZAWA

Advance publication

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Abstract

We consider a $C^r$ diffeomorphism having a Hopf point with $r\ge 5$. If there exists a homoclinic orbit associated with the Hopf point, we say that the diffeomorphism has a \emph{Hopf-homoclinic cycle}. In this paper we prove that every $C^r$ diffeomorphism having a Hopf-homoclinic cycle can be $C^r$ approximated by diffeomorphisms with heterodimensional cycles. Moreover, we study stabilizations of such heterodimensional cycles.

Article information

Source
Tokyo J. Math., Advance publication (2019), 21 pages.

Dates
First available in Project Euclid: 6 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1533520824

Subjects
Primary: 37C05: Smooth mappings and diffeomorphisms
Secondary: 37C20: Generic properties, structural stability 37C29: Homoclinic and heteroclinic orbits

Citation

TOMIZAWA, Shuntaro. Hopf-homoclinic Bifurcations and Heterodimensional Cycles. Tokyo J. Math., advance publication, 6 August 2018. https://projecteuclid.org/euclid.tjm/1533520824


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