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December 2019 Hopf-homoclinic Bifurcations and Heterodimensional Cycles
Shuntaro TOMIZAWA
Tokyo J. Math. 42(2): 449-469 (December 2019). DOI: 10.3836/tjm/1502179284

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 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.

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Shuntaro TOMIZAWA. "Hopf-homoclinic Bifurcations and Heterodimensional Cycles." Tokyo J. Math. 42 (2) 449 - 469, December 2019. https://doi.org/10.3836/tjm/1502179284

Information

Published: December 2019
First available in Project Euclid: 6 August 2018

zbMATH: 07209629
MathSciNet: MR4106588
Digital Object Identifier: 10.3836/tjm/1502179284

Subjects:
Primary: 37C05
Secondary: 37C20, 37C29

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

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Vol.42 • No. 2 • December 2019
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