Symbolic Dynamics of Homoclinic Orbits in a Symmetric Map

Zai-Qiao Bai, Wei-Mou Zheng

Symbolic dynamics for homoclinic orbits in the two-dimensional symmetric map, $x_{n+1}+c{x}_n+x_{n-1}=3x_n^3$, is discussed. Above a critical $c^{\ast }$, the system exhibits a fu…