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arXiv · 1510.04624

Equilibrium measures for certain isometric extensions of Anosov systems

Ralf Spatzier·Daniel Visscher
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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 Holder continuous potential that is constant on fibers, there is a unique equilibrium measure. We prove a similar result for automorphisms of the Heisenberg manifold fibering over the torus. Our methods also give an alternate proof of Brin and Gromov's result on the ergodicity of these frame flows.

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Ralf Spatzier, Daniel Visscher. 2015-10-15. Equilibrium measures for certain isometric extensions of Anosov systems. https://doi.org/10.1017/etds.2016.62

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