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일정

Ergodic Theory and Dynamical Systems SeminarㅣOpen dynamics on subshifts of finite type

기간 : 2023-03-22 ~ 2023-03-22
시간 : 16:00 ~ 17:00
개최 장소 : Online streaming (Zoom)
개요
Ergodic Theory and Dynamical Systems SeminarㅣOpen dynamics on subshifts of finite type
분야Field
날짜Date 2023-03-22 ~ 2023-03-22 시간Time 16:00 ~ 17:00
장소Place Online streaming (Zoom) 초청자Host
연사Speaker Haritha Cheriyath 소속Affiliation Tata Institute
TOPIC Ergodic Theory and Dynamical Systems SeminarㅣOpen dynamics on subshifts of finite type
소개 및 안내사항Content

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. It has attracted the attention of researchers since then especially due to its wide applications.
In this talk, we consider an irreducible subshift of finite type and study the average rate at which the orbits escape into the hole (termed as the escape rate). This problem turns out to be an interesting application of a combinatorial question of counting the number of words of given length not containing any of the words from a fixed collection as subwords. Using this, we compare the escape rates into different holes. We also present some applications of our results in computing the Perron eigenvalues and eigenvectors of any non-negative integer matrix and obtaining a combinatorial expression for the unique measure of maximal entropy on a subshift of finite type.

 

 

https://us02web.zoom.us/j/82314084603?pwd=MzNrRzc5TXl2NFZRTGNXUWd4dWNJQT09

ID: 823 1408 4603
PW: setds23​
학회명Field Ergodic Theory and Dynamical Systems SeminarㅣOpen dynamics on subshifts of finite type
날짜Date 2023-03-22 ~ 2023-03-22 시간Time 16:00 ~ 17:00
장소Place Online streaming (Zoom) 초청자Host
소개 및 안내사항Content

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. It has attracted the attention of researchers since then especially due to its wide applications.
In this talk, we consider an irreducible subshift of finite type and study the average rate at which the orbits escape into the hole (termed as the escape rate). This problem turns out to be an interesting application of a combinatorial question of counting the number of words of given length not containing any of the words from a fixed collection as subwords. Using this, we compare the escape rates into different holes. We also present some applications of our results in computing the Perron eigenvalues and eigenvectors of any non-negative integer matrix and obtaining a combinatorial expression for the unique measure of maximal entropy on a subshift of finite type.

 

 

https://us02web.zoom.us/j/82314084603?pwd=MzNrRzc5TXl2NFZRTGNXUWd4dWNJQT09

ID: 823 1408 4603
PW: setds23​
성명Field Ergodic Theory and Dynamical Systems SeminarㅣOpen dynamics on subshifts of finite type
날짜Date 2023-03-22 ~ 2023-03-22 시간Time 16:00 ~ 17:00
소속Affiliation Tata Institute 초청자Host
소개 및 안내사항Content

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. It has attracted the attention of researchers since then especially due to its wide applications.
In this talk, we consider an irreducible subshift of finite type and study the average rate at which the orbits escape into the hole (termed as the escape rate). This problem turns out to be an interesting application of a combinatorial question of counting the number of words of given length not containing any of the words from a fixed collection as subwords. Using this, we compare the escape rates into different holes. We also present some applications of our results in computing the Perron eigenvalues and eigenvectors of any non-negative integer matrix and obtaining a combinatorial expression for the unique measure of maximal entropy on a subshift of finite type.

 

 

https://us02web.zoom.us/j/82314084603?pwd=MzNrRzc5TXl2NFZRTGNXUWd4dWNJQT09

ID: 823 1408 4603
PW: setds23​
성명Field Ergodic Theory and Dynamical Systems SeminarㅣOpen dynamics on subshifts of finite type
날짜Date 2023-03-22 ~ 2023-03-22 시간Time 16:00 ~ 17:00
호실Host 인원수Affiliation Haritha Cheriyath
사용목적Affiliation 신청방식Host Tata Institute
소개 및 안내사항Content

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. It has attracted the attention of researchers since then especially due to its wide applications.
In this talk, we consider an irreducible subshift of finite type and study the average rate at which the orbits escape into the hole (termed as the escape rate). This problem turns out to be an interesting application of a combinatorial question of counting the number of words of given length not containing any of the words from a fixed collection as subwords. Using this, we compare the escape rates into different holes. We also present some applications of our results in computing the Perron eigenvalues and eigenvectors of any non-negative integer matrix and obtaining a combinatorial expression for the unique measure of maximal entropy on a subshift of finite type.

 

 

https://us02web.zoom.us/j/82314084603?pwd=MzNrRzc5TXl2NFZRTGNXUWd4dWNJQT09

ID: 823 1408 4603
PW: setds23​
Admin Admin · 2023-03-12 22:46 · 조회 203
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