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February 2008 Existence of horseshoe sets with nondegenerate one-sided homoclinic tangencies in ${\mathbb R}^{3}$
Yusuke NISHIZAWA
Hokkaido Math. J. 37(1): 133-145 (February 2008). DOI: 10.14492/hokmj/1253539582

Abstract

In this paper, we present some class of three dimensional $C^{\infty}$ diffeomorphisms with nondegenerate one-sided homoclinic tangencies $q$ associated with hyperbolic fixed points $p$ each of which exhibits a horseshoe set. A key point in the proof is the existence of a transverse homoclinic point arbitrarily close to $q$. This result together with Birkhoff-Smale Theorem implies the existence of a horseshoe set arbitrarily close to $q$.

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Yusuke NISHIZAWA. "Existence of horseshoe sets with nondegenerate one-sided homoclinic tangencies in ${\mathbb R}^{3}$." Hokkaido Math. J. 37 (1) 133 - 145, February 2008. https://doi.org/10.14492/hokmj/1253539582

Information

Published: February 2008
First available in Project Euclid: 21 September 2009

zbMATH: 1147.37017
MathSciNet: MR2395080
Digital Object Identifier: 10.14492/hokmj/1253539582

Subjects:
Primary: 37D10
Secondary: 37C05, 37C15, 37D40

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics

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Vol.37 • No. 1 • February 2008
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