Typical return times in dynamical systems

Recurrence is one of the key concepts in topological dynamics, ergodic and information theories. Especially, limit distributions of return times in dynamical systems and stationary processes have been intensively studied. This field covers fundamental mathematical theorems as well as important apllications, e.g. Lempel-Ziv algorithm for data compression, practically used in format pdf, gif or tiff. However, the question about typical limit distributions of return times for processes derived from a given dynamical system is still open. The goal of this project is to find these typical distributions and establish corresponding classification of dynamical systems. This will be compared with other fundamental invariants, like entropy, and mixing properties. The expected results are believed to contribute to better understanding and evaluating efficiency of LZ algorithm.