PreprintCC0arXiv
Abundance of typical horseshoes for the random standard map
Abstract
We introduce a notion of typical horseshoe, consisting of a pair of rectangles admitting Markov returns at times of positive lower density, with controlled hyperbolic geometry and orbits that shadow typical trajectories. We prove the abundance of typical horseshoes for the random standard map and establish several statistical properties of the system, including exponential mixing and large deviation estimates for the associated projective and two-point processes.
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BibTeX
@misc{tenaglia2026abundance,
title = {{Abundance of typical horseshoes for the random standard map}},
author = {Giuseppe Tenaglia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12908},
eprint = {2609.12908},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12908},
note = {CC0},
}
RIS
TY - UNPB
TI - Abundance of typical horseshoes for the random standard map
AU - Giuseppe Tenaglia
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.12908
UR - https://arxiv.org/abs/2609.12908
AB - We introduce a notion of typical horseshoe, consisting of a pair of rectangles admitting Markov returns at times of positive lower density, with controlled hyperbolic geometry and orbits that shadow typical trajectories. We prove the abundance of typical horseshoes for the random standard map and establish several statistical properties of the system, including exponential mixing and large deviation estimates for the associated projective and two-point processes.
ER -