Entropy Formulas For Dynamical Systems With Mistakes

Details Entropy Formulas For Dynamical Systems With Mistakes Entropy Formulas For Dynamical Systems With Mistakes

2010-11-04

arxiv.org/abs/1011.1115v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

We study the recurrence to mistake dynamical balls, that is, dynamical balls that admit some errors and whose proportion of errors decrease tends to zero with the length of the dynamical ball. We prove, under mild assumptions, that the measure-theoretic entropy coincides with the exponential growth rate of return times to mistake dynamical balls and that minimal return times to mistake dynamical balls grow linearly with respect to its length.Moreover we obtain averaged recurrence formula for subshifts of finite type and suspension semiflows. Applications include $\beta$-transformations, Axiom A flows and suspension semiflows of maps with a mild specification property. In particular we extend some results from [4, 9, 17] for mistake dynamical balls.

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