Chaotic dynamics for two-dimensional tent maps

被引：14

作者：

Pumarino, Antonio ^{[1
]}

Angel Rodriguez, Jose ^{[1
]}

Carles Tatjer, Joan ^{[2
]}

Vigil, Enrique ^{[1
]}

机构：

[1] Univ Oviedo, Dept Math, E-33007 Oviedo, Spain

[2] Univ Politecn Cataluna, Dept Matemat Aplicada & Anal, E-08080 Barcelona, Spain

来源：

NONLINEARITY | 2015年 / 28卷 / 02期

关键词：

piecewise linear maps; strange attractors; invariant measures; CONTINUOUS INVARIANT-MEASURES; DIFFEOMORPHISMS; ATTRACTORS;

D O I：

10.1088/0951-7715/28/2/407

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a two-dimensional extension of the classical one-dimensional family of tent maps, we prove the existence of an open set of parameters for which the respective transformation presents a strange attractor with two positive Lyapounov exponents. Moreover, periodic orbits are dense on this attractor and the attractor supports a unique ergodic invariant probability measure.

引用

页码：407 / 434

页数：28

共 18 条

[11]

KELLER G, 1979, CR ACAD SCI A MATH, V289, P625

[12] EXISTENCE OF INVARIANT MEASURES FOR PIECEWISE MONOTONIC TRANSFORMATIONS [J].

LASOTA, A ;

YORKE, JA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 186 (459) :481-488

[13]

Mira C., 1996, Chaotic Dynamics in Two-Dimensional Noninvertible Maps, DOI DOI 10.1142/2252

[14] Attractors for return maps near homoclinic tangencies of three-dimensional dissipative diffeomorphisms [J].

Pumarino, Antonio ;

Tatjer, Joan Carles .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2007, 8 (04) :971-1005

[15] Dynamics near homoclinic bifurcations of three-dimensional dissipative diffeomorphisms [J].

Pumarino, Antonio ;

Tatjer, Joan Carles .

NONLINEARITY, 2006, 19 (12) :2833-2852

[16] EXPANDING BAKER MAPS AS MODELS FOR THE DYNAMICS EMERGING FROM 3D-HOMOCLINIC BIFURCATIONS [J].

Pumarino, Antonio ;

Angel Rodriguez, Jose ;

Carles Tatjer, Joan ;

Vigil, Enrique .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, 19 (02) :523-541

[17] Absolutely continuous invariant measures for multidimensional expanding maps [J].

Saussol, B .

ISRAEL JOURNAL OF MATHEMATICS, 2000, 116 (1) :223-248

[18]

Tatjer JC, 2001, ERGOD THEOR DYN SYST, V21, P249

← 1 2 →