Bifurcation of a heterodimensional cycle with weak inclination flip

Zhiqin Qiao; Deming Zhu; Qiuying Lu

doi:10.3934/dcdsb.2012.17.1009

Article Contents

2012, Volume 17, Issue 3: 1009-1025. Doi: 10.3934/dcdsb.2012.17.1009

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Bifurcation of a heterodimensional cycle with weak inclination flip

1.
Department of Mathematics, North University of China, Taiyuan, 030051
2.
Department of Mathematics, East China Normal University, Shanghai, 200241
3.
Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018

Received: December 31, 2010

Revised: July 31, 2011

Published: April 2012

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Abstract

Local moving frame is constructed to analyze the bifurcation of a heterodimensional cycle with weak inclination flip in $\mathbb{R}^4$. Under some generic hypotheses, the existence conditions for the heteroclinic orbit, $1$-homoclinic orbit, $1$-periodic orbit and two-fold or three-fold $1$-periodic orbit are given, respectively.

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Mathematics Subject Classification: Primary: 34C23, 37G10; Secondary: 34D09.

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References

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