New type of heteroclinic tangency in two-dimensional maps |
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Authors: | Yoshihiro Yamaguchi Kiyotaka Tanikawa |
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Institution: | (1) Liberal Arts and Sciences, Teikyo University of Technology, Ichihara, 290-01 Chiba, Japan;(2) Division of Theoretical Astrophysics, National Astronomical Observatory, Mitaka, 181 Tokyo, Japan |
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Abstract: | A new mechanism of heteroclinic tangency is investigated by using two-dimensional maps. First, it is numerically shown that the unstable manifold from a hyperbolic fixed point accumulates to the stable manifold of a nearby period-2 hyperbolic point in a piecewise linear map and that the unstable manifold from a hyperbolic fixed point accumulates to the accumulation of the stable manifold of a nearby period-2 hyperbolic point in a cubic map. Second, a theorem on the impossibility of heteroclinic tangency (in the usual sense) is given for a particular type of map. The notions ofdirect andasymptotic heteroclinic tangencies are introduced and heteroclinic tangency is classified into four types. |
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Keywords: | Direct heteroclinic tangency asymptotic heteroclinic tangency stable and unstable manifolds hyperbolic fixed point basin |
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