Shortest distance between multiple orbits and generalized fractal dimensions
Dynamical Systems
2019-12-17 v1 Information Theory
math.IT
Probability
Abstract
We consider rapidly mixing dynamical systems and link the decay of the shortest distance between multiple orbits with the generalized fractal dimension. We apply this result to multidimensional expanding maps and extend it to the realm of random dynamical systems. For random sequences, we obtain a relation between the longest common substring between multiple sequences and the generalized R\'enyi entropy. Applications to Markov chains, Gibbs states and the stochastic scrabble are given.
Keywords
Cite
@article{arxiv.1912.07516,
title = {Shortest distance between multiple orbits and generalized fractal dimensions},
author = {Vanessa Barros and Jerome Rousseau},
journal= {arXiv preprint arXiv:1912.07516},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1808.00078