Transitivity of Heisenberg group extensions of hyperbolic systems

被引：3

作者：

Melbourne, Ian ^{[1
]}

Nitica, Viorel ^{[2
,3
]}

Toeroek, Andrei ^{[3
,4
]}

机构：

[1] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England

[2] W Chester Univ, Dept Math, W Chester, PA 19383 USA

[3] Acad Romana, Inst Math, RO-70700 Bucharest, Romania

[4] Univ Houston, Dept Math, Houston, TX 77204 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2012年 / 32卷

基金：

英国工程与自然科学研究理事会;

关键词：

STABLE TRANSITIVITY; NONCOMPACT EXTENSIONS; DIFFEOMORPHISMS;

D O I：

10.1017/S014338571000091X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that among C-r extensions (r > 0) of a uniformly hyperbolic dynamical system with fiber the standard real Heisenberg group H-n of dimension 2(n) + 1, those that avoid an obvious obstruction to topological transitivity are generically topologically transitive. Moreover, if one considers extensions with fiber a connected nilpotent Lie group with a compact commutator subgroup (for example H-n/Z), among those that avoid the obvious obstruction, topological transitivity is open and dense.

引用

页码：223 / 235

页数：13

共 13 条

[1]

[Anonymous], 1979, FUNDAMENTALS THEORY

[2] The Walters condition [J].

Bousch, T .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2001, 34 (02) :287-311

[3] Stable ergodicity for smooth compact Lie group extensions of hyperbolic basic sets [J].

Field, M ;

Melbourne, I ;

Török, A .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 :517-551

[4]

Katok A., 1995, INTRO MODERN THEORY, DOI 10.1017/CBO9780511809187

[5]

Melbourne I, 2006, DISCRETE CONT DYN-A, V14, P355

[6] Stable transitivity of certain noncompact extensions of hyperbolic systems [J].

Melbourne, I ;

Nitica, V ;

Török, A .

ANNALES HENRI POINCARE, 2005, 6 (04) :725-746

[7] Stable transitivity of Euclidean group extensions [J].

Melbourne, I ;

Nicol, M .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2003, 23 :611-619

[8] Transitivity of Euclidean-type extensions of hyperbolic systems [J].

Melbourne, I. ;

Nitica, V. ;

Torok, A. .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2009, 29 :1585-1602

[9] Transitivity of euclidean extensions of anosov diffeomorphisms [J].

Nitica, V ;

Pollicottt, M .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 :257-269

[10] An open dense set of stably ergodic diffeomorphisms in a neighborhood of a non-ergodic one [J].

Nitica, V ;

Török, A .

TOPOLOGY, 2001, 40 (02) :259-278

← 1 2 →