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Pressure for the space of average pseudo-orbits with block sub-additive potentials

  • Fangzhou Cai
  • Jie Li
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Abstract

In this paper, we introduce the concept of block sub-additive potentials and study pressures on spaces of average pseudo-orbits for ℤ+-actions generated by continuous surjections on compact metric spaces. Relative to each finite open cover, we define topological and measure-theoretic pressures and establish a local variational principle. We prove that the local topological pressure coincides with the local pressure of the induced sub-additive potential. For every invariant measure, the local measure-theoretic pressure is bounded above by the measure-theoretic pressure of the induced potential, and equality holds when the measure is ergodic. Moreover, the global topological and measure-theoretic pressures associated with block sub-additive potentials are shown to be the suprema of their local counterparts over finite open covers. Consequently, the global topological pressure coincides with the pressure of the induced sub-additive potential, yielding a global variational principle.

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Cite

BibTeXRIS
BibTeX
@misc{cai2026pressure,
  title = {{Pressure for the space of average pseudo-orbits with block sub-additive potentials}},
  author = {Fangzhou Cai and Jie Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.31787},
  eprint = {2606.31787},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.31787},
}
RIS
TY  - UNPB
TI  - Pressure for the space of average pseudo-orbits with block sub-additive potentials
AU  - Fangzhou Cai
AU  - Jie Li
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2606.31787
UR  - https://arxiv.org/abs/2606.31787
AB  - In this paper, we introduce the concept of block sub-additive potentials and study pressures on spaces of average pseudo-orbits for ℤ_+-actions generated by continuous surjections on compact metric spaces. Relative to each finite open cover, we define topological and measure-theoretic pressures and establish a local variational principle. We prove that the local topological pressure coincides with the local pressure of the induced sub-additive potential. For every invariant measure, the local measure-theoretic pressure is bounded above by the measure-theoretic pressure of the induced potential, and equality holds when the measure is ergodic. Moreover, the global topological and measure-theoretic pressures associated with block sub-additive potentials are shown to be the suprema of their local counterparts over finite open covers. Consequently, the global topological pressure coincides with the pressure of the induced sub-additive potential, yielding a global variational principle.
ER  -