Construction of equilibrium states revisited
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908596885782528 |
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| author | Dong, Changguang Qiao, Qiujie |
| author_facet | Dong, Changguang Qiao, Qiujie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of equilibrium states revisited Dong, Changguang Qiao, Qiujie Dynamical Systems 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. |
| title | Construction of equilibrium states revisited |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.14313 |