Non-smooth saddle-node bifurcations II: Dimensions of strange attractors

被引：10

作者：

Fuhrmann, G. ^{[1
]}

Groeger, M. ^{[2
]}

Jaeger, T. ^{[1
]}

机构：

[1] Tech Univ Dresden, Dept Math, Dresden, Germany

[2] Univ Bremen, Dept Math, Bremen, Germany

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2018年 / 38卷

关键词：

PINCHED SKEW PRODUCTS; NONCHAOTIC ATTRACTORS; CIRCLE MAP; SPACES; SETS; EXPONENTS; EQUATIONS; SYSTEMS; ARNOLD;

D O I：

10.1017/etds.2017.4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows us to describe the topological structure of the attractors and to prove their minimality.

引用

页码：2989 / 3011

页数：23

共 34 条

[1] Rectifiable sets in metric and Banach spaces [J].