On Escape rate for subshift with Markov measure
Dynamical Systems
2024-06-07 v2
Abstract
In this paper, we consider a subshift of finite type with Markov measure. By considering a union of cylinders as holes, we investigate the exponential growth rate of measure of points whose orbits do not escape into the hole over a fixed number of iterations. We present two formulations for this escape rate: one based on the spectral radius of the Hadamard product of a related adjacency matrix and the stochastic matrix with respect to which the Markov measure is defined, and the other utilizing a recurrence relation. These formulations enable a comparative analysis of escape rates into distinct holes.
Cite
@article{arxiv.2401.05118,
title = {On Escape rate for subshift with Markov measure},
author = {Nikita Agarwal and Haritha Cheriyath and Sharvari Neetin Tikekar},
journal= {arXiv preprint arXiv:2401.05118},
year = {2024}
}