Fractal structure of hyperbolic Lipschitzian dynamical systems

In the paper, dynamical systems admitting no smooth structure are studied. A theorem on the semiconjugacy of a Lipschitzian dynamical system to the corresponding topological Markov chain is proved. A new approach to evaluating bounds for the Hausdorff and the Kolmogorov dimensions of the set of nonwandering points from a Markov partition is suggested.