A remark about Sil'nikov saddle-focus homoclinic orbits

Flaviano Battelli; Ken Palmer

doi:10.3934/cpaa.2011.10.817

Article Contents

2011, Volume 10, Issue 3: 817-830. Doi: 10.3934/cpaa.2011.10.817

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A remark about Sil'nikov saddle-focus homoclinic orbits

Flaviano Battelli^1, and
Ken Palmer^2,

1.
Dipartimento di Scienze Matematiche, Facoltà di Ingegneria, Università, Via Brecce Bianche, 1, 60100 Ancona
2.
Department of Mathematics, National Taiwan University, Taipei 106

Received: October 2008

Revised: July 2009

Published: May 2011

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Abstract

In this note we study Sil'nikov saddle-focus homoclinic orbits paying particular attention to four and higher dimensions where two additional conditions are needed. We give equivalent conditions in terms of subspaces associated with the variational equation along the orbit. Then we review Rodriguez's construction of a three-dimensional system with Sil'nikov saddle-focus homoclinic orbits and finally show how to construct higher-dimensional systems with such orbits.

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Mathematics Subject Classification: Primary: 34C27; 37G20; Secondary: 34C28.

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References

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