On constructing Markov partitions by computer
Two methods to construct Markov partitions for two-dimensional systems are proposed. One is based on the existence of a known, or easily accessible by numerical analysis, hyperbolic fixed points; the other one, which is more general, is derived from Bowen's proof of the existence theorem of Markov partitions for hyperbolic systems. The methods are successfully implemented in two cases of hyperbolic systems: the linear automorphism \(\left( \begin{matrix} 1\\ 1\end{matrix} \begin{matrix} 1\\ 2\end{matrix} \right)\) of the 2-torus and a nonlinear perturbation of it. The methods are applied also to the Hénon mapping. In such nonhyperbolic case, however, they produce partitions of the Hénon attractor which lack some essential properties.
scientific article; zbMATH DE number 4013599