| Abstract: |
| This talk is concerned with dynamical zeta functions for two-dimensional finite-to-one sofic shifts, a natural generalization of shifts of finite type. Firstly, the trace operators and rotational matrices are introduced to compute the numbers of periodic patterns for finite-to-one sofic shifts. Then, the zeta function can be represented as an infinite product of rational functions. The results also hold in the coordinates of any unimodulor transformation in general linear groups over integers. Therefore, there is a family of zeta function representations, which is useful to study the natural boundary of zeta functions. This method can apply to higher-dimensional cases. |
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