SPS organises a seminar by Nikita Agarwal

Event From Date: 
Thursday, 14 November 2019
Event End Date: 
Thursday, 14 November 2019
Event Title: 
SPS organises a seminar by Nikita Agarwal
Event Details: 

School of Physical Sciences

 

Title: Escape Rate in Open Dynamical Systems

 

Speaker:   Nikita Agarwal

IISER, Bhopal


Date: 14 –November  -2019

Time:  4:00 pm , Thursday

Venue: Seminar Room, SPS

 

Abstract :Dynamical systems can be broadly classified into closed and open systems. In a closed system, the orbit of every point lies in the state space for all time, whereas in an open system, the orbit of a point may escape from the state space through a hole. Escape rate represents the average rate at which the orbits escape into the hole. Larger the escape rate, faster the orbits terminate. A classical example of this escape phenomena is the motion of a  ball on a billiard table with a hole (pocket).
In this talk, we will present results on an open dynamical system namely a product of expansive Markov maps on an interval with the hole. Such a map is conjugate to a subshift of finite type. For this class of maps, we examine the dependence of the escape rate on the position and the size of the hole, using techniques from ergodic theory, symbolic dynamics and combinatorics. Theoretical results will be illustrated using examples.