Existence of horseshoe sets with nondegenerate one-sided homoclinic tangencies in ${\mathbb R}^{3}$
NISHIZAWA, Yusuke
Hokkaido Math. J., Tome 37 (2008) no. 4, p. 133-145 / Harvested from Project Euclid
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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 $q$.
Publié le : 2008-02-15
Classification:  Horseshoe sets,  Homoclinic tangencies,  Singular \lambda$-Lemma,  Birkhoff-Smale Theorem,  37D10,  37C15,  37C05,  37D40 
@article{1253539582,
     author = {NISHIZAWA, Yusuke},
     title = {Existence of horseshoe sets with nondegenerate one-sided homoclinic tangencies in ${\mathbb R}^{3}$},
     journal = {Hokkaido Math. J.},
     volume = {37},
     number = {4},
     year = {2008},
     pages = { 133-145},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1253539582}
}

NISHIZAWA, Yusuke. Existence of horseshoe sets with nondegenerate one-sided homoclinic tangencies in ${\mathbb R}^{3}$. Hokkaido Math. J., Tome 37 (2008) no. 4, pp.  133-145. http://gdmltest.u-ga.fr/item/1253539582/