A Simple Example of Pathological Foliations in Skew-Product Diffeomorphisms
Dynamical Systems
2024-11-05 v2
Abstract
Inspired by examples of Katok and Milnor \cite{Milnor1997}, we construct simple examples of skew-product volume preserving diffeomorphism where the center foliation is pathological in the sense that, there is a full measure set whose intersection with any center leaf contains at most one point. Comparing with other examples in literature, our mechanism for producing such pathological foliation is simple and elementary.
Keywords
Cite
@article{arxiv.2404.18495,
title = {A Simple Example of Pathological Foliations in Skew-Product Diffeomorphisms},
author = {Zhihong Xia and Peizheng Yu},
journal= {arXiv preprint arXiv:2404.18495},
year = {2024}
}