This research introduces topological pressure and ergodic mass distribution in flows, highlighting implications for measurable potentials.
We introduce the concepts of topological and measure-theoretic pressures for flows with a measurable potential and examine the corresponding variational principle for this topological pressure. Additionally, we present the ergodic mass distribution principle, an inverse variational principle, and several distinct yet equivalent characterizations of measure-theoretic pressures. Furthermore, we explore the pressure associated with frame flows.
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Tang et al. (2025) studied this question.
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