Dynamical complexity of Anosov systems driven by a quasi-periodic force

被引：0
作者：
Wen Huang [1 ]
Zeng Lian [2 ]
Kening Lu [2 ]
机构：
[1] Department of Mathematics,University of Science and Technology of China
[2] School of Mathematics,Sichuan
来源：
Science China(Mathematics) | 2025年 / 68卷 / 01期
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D O I：
暂无
中图分类号：
O19 [动力系统理论]; O211.6 [随机过程];
学科分类号：
070104 ; 0711 ; 071101 ;
摘要：
Consider C2 Anosov systems on a compact manifold driven by a quasi-periodic force.We study their dynamical complexity on various levels from the perspectives of both path-wise dynamics and stochastic processes.Assuming that these systems are non-wandering（i.e.,every point in the phase space is nonwandering）,we prove a set of results:（1） the existence of abundance of random periodic points;（2） a random Liv?ic theorem;（3） a random Ma?é-Bousch-Conze-Guivarc'h lemma;（4） the existence of strong random horseshoes.Additionally,a concrete example constructed on a 2-dimensional torus is also given to uncover some interesting phenomena of the systems.
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页码：89 / 136
页数：48
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