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 $q$.
Citation
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
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