DOI: 10.1063/5.0319679 ISSN: 0022-2488
Conditional measure-theoretic pressure with respect to monotonic partitions
Huihui Li, Jianrong XiaoIn this paper, we introduce various types of conditional Katok pressures with respect to monotonic partitions with sub-additive potentials for an ergodic measure under Bowen metric and Feldman–Katok metric, respectively. We show that these notions coincide with the sum of conditional measure-theoretic entropy and a constant associated with the potentials under tempered variation condition.