Exponential speed of mixing for skew-products with singularities

被引：4

作者：

Markarian, R. ^{[1
]}

Pacifico, M. J. ^{[2
]}

Vieitez, J. L. ^{[3
]}

机构：

[1] Univ Republica, Inst Matemat & Estadist IMERL, Fac Ingn, Montevideo 11300, Uruguay

[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, RJ, Brazil

[3] Univ Republ, Salto 50000, Uruguay

来源：

NONLINEARITY | 2013年 / 26卷 / 01期

关键词：

DECAY;

D O I：

10.1088/0951-7715/26/1/269

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f : [0, 1]\{1/2} x [0, 1] ->[0, 1] x [0, 1] be the C-infinity endomorphism given by f (x, y) = (2x - left perpendicular2xright perpendicular, y + c/vertical bar x - 1/2 vertical bar - left perpendiculary + c/vertical bar x - 1/2 vertical bar right perpendicular), c is an element of IR+. We prove that f is topologically mixing and if c > 1/4 then f is mixing with respect to the Lebesgue measure. Furthermore the speed of mixing is exponential. This skew-product can be seen as a toy model related to Lorenz-like attractors.

引用

页码：269 / 287

页数：19

共 13 条

[1]

[Anonymous], 2006, Chaotic Billiards

[2]

[Anonymous], PUBL MATH I HAUTES E

[3]

Araujo V, 2010, ERGEB MATH GRENZGEB, V53, P1, DOI 10.1007/978-3-642-11414-4

[4]

Benedicks M, 2000, ASTERISQUE, P13

[5] ERGODIC PROPERTIES OF NOWHERE DISPERSING BILLIARDS [J].

BUNIMOVICH, LA .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 65 (03) :295-312

[6]

Chernov N, 2000, ENCYL MATH SCI, V101, P89

[7]

LORENZ EN, 1963, J ATMOS SCI, V20, P130, DOI 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO

[8]

[9] Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers [J].

Morales, CA ;

Pacifico, MJ ;

Pujals, ER .

ANNALS OF MATHEMATICS, 2004, 160 (02) :375-432

[10]

Pesin Y B., 1977, Russian Mathematical Surveys, V32, P55, DOI [10.1070/RM1977v032n04ABEH001639, DOI 10.1070/RM1977V032N04ABEH001639]

← 1 2 →