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Symbolic Dynamics of Homoclinic Orbits in a Symmetric Map | | Zai-Qiao Bai
; Wei-Mou Zheng
; | | Date: |
17 Dec 2001 | | Subject: | Chaotic Dynamics | nlin.CD | | Abstract: | Symbolic 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. | | Source: | arXiv, nlin.CD/0201031 | | Services: | Forum | Review | PDF | Favorites | |
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