Intermediate topological pressures and variational principles for nonautonomous dynamical systems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914529688944640 |
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| author | Ju, Yujun |
| author_facet | Ju, Yujun |
| contents | We introduce a one-parameter family of intermediate topological pressures for nonautonomous dynamical systems which interpolate between the Pesin-Pitskel topological pressure and the lower and upper capacity pressures. The construction is based on the Carathéodory-Pesin structure in which all admissible strings in a covering satisfy $ N \le n < N/θ+ 1 $, where $ θ\in [0,1] $ is a parameter. The extremal cases $θ=0$ and $θ=1$ recover the Pesin-Pitskel pressure and the two capacity pressures, respectively. We first investigate several properties of the intermediate pressure, including proving that it is continuous on $(0, 1]$ but may fail to be continuous at $0$, as well as establishing the power rule and monotonicity. We then derive inequalities for intermediate pressures with respect to the factor map. Finally, we introduce intermediate measure-theoretic pressures and prove variational principles relating them to the corresponding topological pressures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_00182 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Intermediate topological pressures and variational principles for nonautonomous dynamical systems Ju, Yujun Dynamical Systems We introduce a one-parameter family of intermediate topological pressures for nonautonomous dynamical systems which interpolate between the Pesin-Pitskel topological pressure and the lower and upper capacity pressures. The construction is based on the Carathéodory-Pesin structure in which all admissible strings in a covering satisfy $ N \le n < N/θ+ 1 $, where $ θ\in [0,1] $ is a parameter. The extremal cases $θ=0$ and $θ=1$ recover the Pesin-Pitskel pressure and the two capacity pressures, respectively. We first investigate several properties of the intermediate pressure, including proving that it is continuous on $(0, 1]$ but may fail to be continuous at $0$, as well as establishing the power rule and monotonicity. We then derive inequalities for intermediate pressures with respect to the factor map. Finally, we introduce intermediate measure-theoretic pressures and prove variational principles relating them to the corresponding topological pressures. |
| title | Intermediate topological pressures and variational principles for nonautonomous dynamical systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2601.00182 |