Dimension and measure theoretic entropy of a subshift in symbolic space

摘要

WITH the development of the theory of dynamical systems and fractal geometry, one proved that symbolic dynamics is a powerful tool to study chaos and fractals. It is useful to study the fractal characteristics of symbolic dynamics. In the present notewe shall point out the relation between the dimension and measure theoretic entropy of any subshift in symbolic space. We prove here that the Bowen' s formula for Hausdorf f dimension holds without Markov structure. A variational principle for dimensionis obtained.