Symbolic Dynamics of Homoclinic Orbits in a Symmetric Map

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dc.creatorBai, Zai-Qiao
dc.creatorZheng, Wei-Mou
dc.date2002-01-17
dc.date.accessioned2026-07-07T05:33:51Z
dc.date.available2026-07-07T05:33:51Z
dc.descriptionSymbolic dynamics for homoclinic orbits in the two-dimensional symmetric map, $x_{n+1}+cx_{n}+x_{n-1}=3x_{n}^3$, is discussed. Above a critical $c^{\ast}$, the system exhibits a fully-developed horse-shoe so that its global behavior is described by a complete ternary symbolic dynamics. The relative location of homoclinic orbits is determined by their sequences according to a simple rule, which can be used to numerically locate orbits in phase space. With the decrease of $c$, more and more pairs of homoclinic orbits collide and disappear. Forbidden zone in the symbolic space induced by the collision is discussed.
dc.description11 pages 5 figures
dc.identifierhttps://arxiv.org/abs/nlin/0201031
dc.identifierhttp://arxiv.org/abs/nlin/0201031
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80151
dc.subjectChaotic Dynamics
dc.titleSymbolic Dynamics of Homoclinic Orbits in a Symmetric Map
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