On the Abundance of Chaotic Behavior for Generic One-Parameter Families of Maps

作     者：Zheng Zhiming Department of Mathematics Peking University Beijing, 100871 China 

作者机构：Department of Mathematics Peking University Beijing China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1996年第12卷第4期

页      面：398-412页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by the NSFC and the National 863 Project 

主　　题：Chaos Generic regular family Probability measure 

摘      要：In this paper, we want to show the abundance of chaotic systems with absolutely continuous probability measures in the generic regular family with perturbable points. More precisely, we prove that if fa:I→I, a∈P is a regular family satisfying some conditions described in the next section, then there exists a Borel set Ω(?)P of positive Lebesgue measure such that for every a∈Ω, fa admits an absolutely continuous invariant probability measure w.r.t. the Lebesgue measure. The idea of proof in this paper, as compared with that shown in [1] and [7], follows a similar line.