Abstract: In this talk, we present two main results on entropy perturbations of subshifts of finite type. First, we describe a general upper bound for the entropy loss when a finite collection of admissible words is forbidden. The bound depends on the Perron eigenvalue and a generating function associated with the forbidden set, and is obtained using the Parry measure together with a blocking argument to control the growth of admissible words that avoid the forbidden patterns. Second, we explain the asymptotic behavior when the minimal length of the forbidden words tends to infinity. Under suitable growth conditions on the number of forbidden words, the entropy difference tends to zero. In particular, if the forbidden words become sufficiently long, the entropy of the perturbed system converges to that of the original shift.

Organizer: Jung-Chao Ban (NCCU)