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Equilibrium measures for certain isometric extensions of Anosov systems

Published online by Cambridge University Press:  22 September 2016

RALF SPATZIER  and
DANIEL VISSCHER
RALF SPATZIER
Affiliation:
University of Michigan, Department of Mathematics, 530 Church Street, Ann Arbor, Michigan 48109, USA email spatzier@umich.edu, davissch@umich.edu
DANIEL VISSCHER
Affiliation:
University of Michigan, Department of Mathematics, 530 Church Street, Ann Arbor, Michigan 48109, USA email spatzier@umich.edu, davissch@umich.edu
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Abstract

We prove that for the frame flow on a negatively curved, closed manifold of odd dimension other than 7, and a Hölder 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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 3 , May 2018 , pp. 1154 - 1167
Copyright
© Cambridge University Press, 2016 

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