Entropy drop for perturbartion of subshift of finite type (CONTRIBUTED TALK)
speaker: Harita Cheriath (University of Chile)abstract: For a finite symbol set A, a subshift X is a closed shift-invariant subset of the bi-infinite sequence AZ. If a finite word with symbols from A is a subword of some sequence in X, it is said to be allowed. When the subshift is perturbed by making some allowed words as forbidden, the topological entropy of the resulting system reduces. In this talk, we investigate this drop in topological entropy when X is a subshift of finite type (SFT). Such a study on an SFT is helpful as it models a large class of complex dynamical systems. Given that the entropy of a subshift is determined by the exponential growth rate of the count of allowed words of fixed length, this issue can be reformulated as an enumeration problem. We use combinatorial techniques to compare the difference in entropies when words of equal lengths are forbidden. We also see an alternate measure-theoretic interpretation of this problem where the newly forbidden words correspond to holes in X and this difference in entropy is the rate at which the orbits escape into the hole with respect to its measure of maximal entropy. We also look at the case when the length of this newly forbidden words increases, which results in such a hole to converge to union of points.
timetable:
Mon 20 May, 16:30 - 17:00, Aula Dini
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