Generalized Fiber Contraction Mapping Principle
Dynamical Systems
2024-12-16 v1
Abstract
We prove a generalized non-stationary version of the fiber contraction mapping theorem. It was originally used in [HirschPugh70] to prove that the stable foliation of a Anosov diffeomorphism of a surface is . Our generalized principle is used in [Luna24], where an analogous regularity result for stable foliations of non-stationary systems is proved. The result is stated in a general setting so that it may be used in future dynamical results in the random and non-stationary settings, especially for graph transform arguments.
Cite
@article{arxiv.2412.09767,
title = {Generalized Fiber Contraction Mapping Principle},
author = {Alexandro Luna and Weiran Yang},
journal= {arXiv preprint arXiv:2412.09767},
year = {2024}
}