稳健可达双曲排斥集  

Robust Accessible Hyperbolic Repelling Sets

作　　者：肖建荣 Xiao Jianrong(Center for Mathematical Sciences and Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070;School of Mathematical Sciences,Xiamen University,Fujian Xiamen 361005)

机构地区：[1]武汉理工大学理学院数学科学研究中心与数学系,武汉430070 [2]厦门大学数学科学学院,福建厦门361005

出　　处：《数学物理学报（A辑）》2024年第1期1-11,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(12271418)。

摘　　要：该文通过对一个分段线性满射实施Denjoy-like手术,构造了一簇C1映射fα(1 <α <3),使其具有以下性质1)fα具有一个有正Lebesgue测度的双曲排斥Cantor集Aα,且Aα也是fα的非正则吸引子;2)吸引子Aα是可达的:吸引盆B(Aα)与Aα的差集B(Aα)Aα具有正Lebesgue测度;3)该簇映射结构稳定:对不同的α与α’,fα与fα’拓扑共轭.该手术需要将不连续点爆破,并将不连续点的原像集的所有点替换成开区间.fα的C1光滑性由这些区间长度的精确控制以及区间上映射的细致定义保证.By operating Denjoy like surgery on a piecewise linear map,we constructed a family of Cl maps fα(1<α<3)admitting the following properties:1)fa admits a hyperbolic repelling Cantor set Aαwith positive Lebesgue measure,and Aαis also a wild attractor of fα;2)The attractor Aαis accessible:the difference set B(Aa)\A between the basin of attraction B(Aa)and Aαhas positive Lebesgue measure;3)The family is structurally stable:fαis topologically conjugate to fa,for all 1<α,Q'<3.The surgery involves blowing up the discontinuity and its preimages set into open intervals.The Ci smoothness of f&is ensured by the prescribed lengths of glued intervals and the maps defined on the glued intervals.

关 键 词：双曲排斥集 非正则吸引子 Denjoy-like手术 稳健 可达 

分 类 号：O193[理学—数学]