Random Markov partitions for non-uniformly expanding systems with additive diffusive noise
File(s)
Author(s)
Tenaglia, Giuseppe
Type
Thesis
Abstract
We introduce the concept of random horseshoes and establish both the density of random horseshoes and the existence of a random Gibbs-Markov map with an exponential tail for non-uniformly expanding random dynamical systems influenced by additive noise. To accomplish this, we leverage the framework of Young times and demonstrate how this tool directly establishes the existence of a random Young tower and the density of random horseshoes. Statement of main hypotheses and results is in chapter II. Chapters III and IV, respectively,show, for random systems with additive diffusive noise, on large deviation estimates for unbounded observables and annealed transitivity properties for balls of fixed size. These results are key to proving, in Chapter V, the existence and the exponential tail estimates of Young times. In Chapter VI, we apply Young times to derive the density of random horseshoes and in chapter VII we prove the existence of the Gibbs-Markov map. Finally, in Chapter VIII, we write a summary of the results and outline possible future research directions.
Version
Open Access
Date Issued
2025-08-22
Date Awarded
01/11/2025
License URL
Advisor
Turaev, Dmitry
Lamb, Jeroen
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)