PreprintCC BY 4.0arXiv
On record behaviours of returns for interval maps
Abstract
Given a dynamical system (X,T) and an ergodic invariant measure μ, a μ-typical point x∈ X under T visits arbitrarily small neighbourhood of x. We will use techniques based on extreme value theory and Laplace functional for point process to show that, for interval maps with suitable mixing and anti-clustering conditions, the limiting distributions of the record times and values of the return process Yj(x)=−log d(Tjx,x), after possible normalisation, has Poisson-type laws.
Related
BibTeX
@misc{zhao2026record,
title = {{On record behaviours of returns for interval maps}},
author = {Boyuan Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39928},
eprint = {2610.39928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39928},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On record behaviours of returns for interval maps
AU - Boyuan Zhao
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39928
UR - https://arxiv.org/abs/2610.39928
AB - Given a dynamical system (X,T) and an ergodic invariant measure μ, a μ-typical point x∈ X under T visits arbitrarily small neighbourhood of x. We will use techniques based on extreme value theory and Laplace functional for point process to show that, for interval maps with suitable mixing and anti-clustering conditions, the limiting distributions of the record times and values of the return process Y_j(x)=−log d(T^jx,x), after possible normalisation, has Poisson-type laws.
ER -