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arXiv · 2512.15253

On equilibrium states for certain partially hyperbolic endomorphisms with one-dimensional center

Yifan Zhang·Yujun Zhu
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Abstract

In this paper, the equilibrium states for a non-degenerate $ C^2 $ partially hyperbolic endomorphism $f$ on a closed Riemannian manifold $M$ with one-dimensional center bundle are investigated. Applying the criterion of Climenhaga-Thompson (\cite{CT21}) and the method of Mongez-Pacifico (\cite{Mongez}), we use the techniques of inverse limit to obtain the uniqueness and robustness of equilibrium states for $f$ and any H\"{o}lder continuous potential satisfying certain conditions about the unstable pressure and stable pressure.

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Yifan Zhang, Yujun Zhu. 2025-12-17. On equilibrium states for certain partially hyperbolic endomorphisms with one-dimensional center. https://arxiv.org/abs/2512.15253

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