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arXiv · 2510.14313

Construction of equilibrium states revisited

Changguang Dong·Qiujie Qiao
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Abstract

In [52], Parmenter and Pollicott establish an abstract criterion that gives a geometric construction of equilibrium states for a class of partially hyperbolic systems. We refine their criterion to cover a much broader class of diffeomorphisms, which include certain diffeomorphisms with exponential mixing property (with respect to volume), Katok maps and ``almost Anosov'' diffeomorphisms. As a special case, we obtain a construction of equilibrium states for ergodic partially hyperbolic affine maps/flows on homogeneous spaces, without any restrictions on the orbit growth along center directions.

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Changguang Dong, Qiujie Qiao. 2025-10-16. Construction of equilibrium states revisited. https://arxiv.org/abs/2510.14313

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