To measure the complexity of a “non-invertible” continuous map f on a compact metric space
via the preimage structure, Hurley introduced the notion of pointwise topological preimage …

In this paper, entropy, pressure and equilibrium states are investigated for noninvertible
random dynamical systems via the preimage structure. For a continuous random dynamical …

We investigate conditional entropy with respect to monotonic (invariant, decreasing, or
increasing) measurable partitions. In particular, we obtain Brin-Katok's and Katok's entropy …

Full article: Conditional Brin-Katok's entropy formula for monotonic partitions on Feldman-Katok
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In this paper, pointwise preimage pressures for (non-invertible) continuous maps on any
subset (not necessarily compact or invariant) are introduced via Carathéodory-Pesin …

It is well-known that for topological dynamical systems $\epsilon $-stable sets have a deep
connection with the topological entropy of the systems. In the present paper, we investigate …

We propose a new definition of preimage entropy dimension for continuous maps on
compact metric spaces, investigate fundamental properties of the preimage entropy …