Equilibrium measures for certain isometric extensions of Anosov systems

被引:7
作者
Spatzier, Ralf [1 ]
Visscher, Daniel [1 ]
机构
[1] Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA
基金
美国国家科学基金会;
关键词
GEODESIC-FLOWS; FRAME FLOWS; INVARIANT-MEASURES; HIGHER-RANK; ERGODICITY; UNIQUENESS; CONTINUITY; MANIFOLDS; ENTROPY;
D O I
10.1017/etds.2016.62
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove that for the frame flow on a negatively curved, closed manifold of odd dimension other than 7, and a Holder continuous potential that is constant on fibers, there is a unique equilibrium measure. Brin and Gromov's theorem on the ergodicity of frame flows follows as a corollary. Our methods also give a corresponding result for automorphisms of the Heisenberg manifold fibering over the torus.
引用
收藏
页码:1154 / 1167
页数:14
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