Rigorous and effective numerics for Liverani-Saussol-Vaienti maps
Abstract
We make highly accurate numerical estimates of basic properties of the invariant measure for Liverani-Saussol-Vaienti intermittent maps, an archetypal slowly mixing dynamical system. We solve the challenge of precise and efficient estimation for a map with non-uniform expansion, where the transfer operator does not have a spectral gap. We do this using an Abel function, which solves the neutral dynamics, and which we can compute accurately via an asymptotic expansion. Our work covers both finite and sigma-finite invariant measure cases. In particular, we obtain the first practical estimates for the parameter far from zero, including the sigma-finite case. This opens the door to much deeper numerical study of intermittent dynamics than was previously possible. A driving motivation for this work is the upcoming proof of optimal rates of memory loss which works equally for finite and infinite invariant measure cases. No prior results on rates of memory loss for dynamical systems with infinite invariant measure exist, with a single exception of a recent paper by I.Chevyrev and A.K. on null recurrent Markov chains.
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BibTeX
@misc{korepanov2026rigorous,
title = {{Rigorous and effective numerics for Liverani-Saussol-Vaienti maps}},
author = {Alexey Korepanov and YuTong Wei and Caroline Wormell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01879},
eprint = {2610.01879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01879},
}
RIS
TY - UNPB
TI - Rigorous and effective numerics for Liverani-Saussol-Vaienti maps
AU - Alexey Korepanov
AU - YuTong Wei
AU - Caroline Wormell
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01879
UR - https://arxiv.org/abs/2610.01879
AB - We make highly accurate numerical estimates of basic properties of the invariant measure for Liverani-Saussol-Vaienti intermittent maps, an archetypal slowly mixing dynamical system. We solve the challenge of precise and efficient estimation for a map with non-uniform expansion, where the transfer operator does not have a spectral gap. We do this using an Abel function, which solves the neutral dynamics, and which we can compute accurately via an asymptotic expansion. Our work covers both finite and sigma-finite invariant measure cases. In particular, we obtain the first practical estimates for the parameter far from zero, including the sigma-finite case. This opens the door to much deeper numerical study of intermittent dynamics than was previously possible. A driving motivation for this work is the upcoming proof of optimal rates of memory loss which works equally for finite and infinite invariant measure cases. No prior results on rates of memory loss for dynamical systems with infinite invariant measure exist, with a single exception of a recent paper by I.Chevyrev and A.K. on null recurrent Markov chains.
ER -