发表机构
Great Bay University; University of Science and Technology of China; The University of Sydney（大湾区大学; 中国科学技术大学; 悉尼大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对 Liverani-Saussol-Vaienti 间歇映射，利用 Abel 函数和渐近展开，实现了对不变测度性质的高精度数值估计，首次覆盖参数远离零及 sigma-有限情形，为间歇动力学数值研究和记忆丧失速率证明奠定基础。
AI 中文摘要
我们对 Liverani-Saussol-Vaienti 间歇映射（一种典型的慢混合动力系统）的不变测度的基本性质进行了高精度的数值估计。我们解决了对于具有非均匀扩张且转移算子没有谱间隙的映射进行精确高效估计的挑战。我们使用 Abel 函数来解决中性动力学问题，该函数可以通过渐近展开精确计算。我们的工作涵盖了有限和 sigma-有限不变测度两种情况。特别地，我们首次获得了参数远离零时的实用估计，包括 sigma-有限情形。这为比以往更深入的间歇动力学数值研究打开了大门。这项工作的一个主要动机是即将完成的关于记忆丧失最优速率的证明，该证明同样适用于有限和无限不变测度情形。此前，对于具有无限不变测度的动力系统，除了最近一篇关于零常返马尔可夫链的论文（由 this http URL 和 A.K. 撰写）外，没有任何关于记忆丧失速率的结果。
英文摘要
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.
