Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Subshifts of finite type with a hole: properties and applications
Speaker: Haritha Cheriyath, TIFR
Date: September 1, 2021
Time: 17:00:00 Hours
Venue: AG-77
Abstract: Dynamical systems can be broadly classified into closed and open systems. In a (traditional) closed system, the orbit of a point lies in the state space for all time, whereas in an open system, the orbit of a point may eventually escape from the state space through a hole. The notion of open dynamical systems was introduced by Pianigiani and Yorke in 1979, motivated by the dynamics of a ball on a billiard table with pockets. In this talk, we consider an irreducible subshift of finite type and study the average rate at which the orbits escape into the hole. This problem turns out to be an interesting application of a combinatorial problem which is counting the number of words of fixed length not containing any of the words from a fixed collection as subwords. We also present some applications of our results in computing the Perron eigenvalues and eigenvectors of any irreducible (0-1) matrix and obtaining a combinatorial expression for the Parry measure of a subshift of finite type.
Title of Talk: Subshifts of finite type with a hole: properties and applications
Speaker: Haritha Cheriyath, TIFR
Date: September 1, 2021
Time: 17:00:00 Hours
Venue: AG-77
Abstract: Dynamical systems can be broadly classified into closed and open systems. In a (traditional) closed system, the orbit of a point lies in the state space for all time, whereas in an open system, the orbit of a point may eventually escape from the state space through a hole. The notion of open dynamical systems was introduced by Pianigiani and Yorke in 1979, motivated by the dynamics of a ball on a billiard table with pockets. In this talk, we consider an irreducible subshift of finite type and study the average rate at which the orbits escape into the hole. This problem turns out to be an interesting application of a combinatorial problem which is counting the number of words of fixed length not containing any of the words from a fixed collection as subwords. We also present some applications of our results in computing the Perron eigenvalues and eigenvectors of any irreducible (0-1) matrix and obtaining a combinatorial expression for the Parry measure of a subshift of finite type.