Quasi-periodically Forced Logistic Map with Weak Liouvillean Frequency  

作　　者：Jin Hao LIANG Lin Lin FU 

机构地区：[1]Department of Applied Mathematics,Nanjing Forestry University,Nanjing 210037,P.R.China [2]School of Mathematics and Statistics,Shaoguan University,Shaoguan 512005,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第10期2411-2435,共25页数学学报（英文版）

基　　金：supported by NSFC(Grant No.12101311);supported by GuangDong Basic and Applied Basic Research Foundation(Grant No.2022A1515110427)。

摘　　要：Consider a class of quasi-periodically forced logistic maps T×[0,1]■:(θ,x)→(θ+ω,c(θ)x(1-x))(T=R/Z),whereωis an irrational frequency and c(θ)is a specific bimodal function.We prove that under weak Liouvillean condition on frequency,the strange non-chaotic attractor occurs with negative Lyapunov exponent.This extends the result in[Bjerklov,CMP,2009].

关 键 词：Quasi-periodically forced logistic map strange non-chaotic attractor weak Liouvillean frequency Lyapunov exponent 

分 类 号：O156.7[理学—数学]