某些纤维部分双曲系统的光滑模型

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2023-11-13 DOI:10.1017/etds.2023.102

MEG DOUCETTE

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引用次数: 3

摘要

摘要证明了在对纤维的限制下，任何纤维在零流形上的部分双曲系统都是叶共轭于光滑模型的，该光滑模型在纤维上是等距的，并在基上下降到双曲零流形自同构。一个成分是独立兴趣的结果，推广了Hiraide的结果:零流形的Anosov同胚拓扑共轭于双曲零流形自同态。

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Smooth models for certain fibered partially hyperbolic systems

Abstract We prove that under restrictions on the fiber, any fibered partially hyperbolic system over a nilmanifold is leaf conjugate to a smooth model that is isometric on the fibers and descends to a hyperbolic nilmanifold automorphism on the base. One ingredient is a result of independent interest generalizing a result of Hiraide: an Anosov homeomorphism of a nilmanifold is topologically conjugate to a hyperbolic nilmanifold automorphism.

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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.