PreprintCC BY-NC-ND 4.0arXiv
Foliations and minimality for twist maps
Abstract
In this paper we consider area-preserving twist maps f:T2→T2 with vertical rotation sets reduced to a single irrational number α. Our first result states that under these hypotheses, there exists a unique f-invariant foliation ℱG={Graph(ϕt)}t∈T1, where each function ϕt:T1→T1 is K-Lipschitz for some constant K=K(f). Moreover, we also prove that if ℱG is a Lipschitz foliation, then f is minimal.
Related
- Puncture-Forgetting Maps for Measured Foliations and Applications in Teichmüller Space and Complex Dynamics
- Length control for foliations by Jordan curves via smooth quasiconformal maps
- Persistence of invariant graphs for twist maps under analytic perturbations
- Generic Linear Momentum Escape for Twist Maps
- Quantitative Persistence and Regularity of Invariant Graphs for Dissipative Twist Maps
BibTeX
@misc{zanata2026foliations,
title = {{Foliations and minimality for twist maps}},
author = {Salvador Addas Zanata and Julian Lazaro Aguirre},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.27102},
eprint = {2609.27102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27102},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Foliations and minimality for twist maps
AU - Salvador Addas Zanata
AU - Julian Lazaro Aguirre
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2609.27102
UR - https://arxiv.org/abs/2609.27102
AB - In this paper we consider area-preserving twist maps f:T^2→T^2 with vertical rotation sets reduced to a single irrational number α. Our first result states that under these hypotheses, there exists a unique f-invariant foliation ℱ_G={Graph(ϕ_t)}_t∈T^1, where each function ϕ_t:T^1→T^1 is K-Lipschitz for some constant K=K(f). Moreover, we also prove that if ℱ_G is a Lipschitz foliation, then f is minimal.
ER -