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Abstract
In this paper, we introduce the Pesin–Pitskel unstable pressure to study dynamical complexity of general subsets in partially hyperbolic systems. We establish some basic results in dimension theory for Pesin–Pitskel unstable pressure, including a pressure distribution principle, and a variational principle for any compact (not necessarily invariant) subset between its Pesin–Pitskel unstable pressure and unstable metric pressure of probability measures supported on this set.
Acknowledgments
We would like to thank the referee for useful comments on this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The first author was supported by the Foundation in higher education institutions of Henan Province, PR China [grant number 19A110030]. The third author was supported by the National Natural Science Foundation of China [grant number 11971236]; China Postdoctoral Science Foundation [grant number 2016M591873], and China Postdoctoral Science Special Foundation [grant number 2017T100384]. The work was also funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. We would like to express our gratitude to Tianyuan Mathematical Center in Southwest China [grant number 11826102], Sichuan University and Southwest Jiaotong University for their support and hospitality.