Cocycles with one exponent over partially hyperbolic systems

被引：34
|
作者：
Kalinin, Boris [1 ]
Sadovskaya, Victoria [1 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
来源：
GEOMETRIAE DEDICATA | 2013年 / 167卷 / 01期
基金：
美国国家科学基金会;
关键词：
Linear cocycle; Lyapunov exponent; Partially hyperbolic system; Amenable reduction; ERGODIC-THEORY;
D O I：
10.1007/s10711-012-9808-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider Holder continuous linear cocycles over partially hyperbolic diffeomorphisms. For fiber bunched cocycles with one Lyapunov exponent we show continuity of measurable invariant conformal structures and sub-bundles. Further, we establish a continuous version of Zimmer's Amenable Reduction Theorem. For cocycles over hyperbolic systems we also obtain polynomial growth estimates for the norm and the quasiconformal distortion from the periodic data.
引用
收藏
页码：167 / 188
页数：22
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