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Yujun Ju

Publications and source records attributed to Yujun Ju.

4 recordsLinked to original sources
arXiv2026

A Variational Principle for the Topological Pressure of Non-autonomous Iterated Function Systems on Subsets

Motivated by the notion of topological entropy for free semigroup actions introduced by Bi\'s, we define the Pesin--Pitskel topological pressure for non-autonomous iterated function systems via the Carath\'eodory--Pesin structure. We show that this Pesin--Pitskel topological pressure coincides with the corresponding weighted topological pressure. Furthermore, we establish a variational principle asserting that, for any nonempty compact subset, the Pesin--Pitskel topological pressure equals the supremum of the associated measure-theoretic pressures over all Borel probability measures supported on that subset.

math.DS↗
arXiv2026

Intermediate topological pressures and variational principles for nonautonomous dynamical systems

We introduce a one-parameter family of intermediate topological pressures for nonautonomous dynamical systems which interpolate between the Pesin-Pitskel topological pressure and the lower and upper capacity pressures. The construction is based on the Carath\'eodory-Pesin structure in which all admissible strings in a covering satisfy $ N \le n < N/\theta + 1 $, where $ \theta \in [0,1] $ is a parameter. The extremal cases $\theta=0$ and $\theta=1$ recover the Pesin-Pitskel pressure and the two capacity pressures, respectively. We first investigate several properties of the intermediate pressure, including proving that it is continuous on $(0, 1]$ but may fail to be continuous at $0$, as well as establishing the power rule and monotonicity. We then derive inequalities for intermediate pressures with respect to the factor map. Finally, we introduce intermediate measure-theoretic pressures and prove variational principles relating them to the corresponding topological pressures.

math.DS↗
arXiv2025

Intermediate topological entropies for subsets of nonautonomous dynamical systems

Motivated by the notion of intermediate dimensions introduced by Falconer et al., we introduce a continuum of topological entropies that are intermediate between the (Bowen) topological entropy and the lower and upper capacity topological entropies. This is achieved by restricting the families of allowable covers in the definition of topological entropy by requiring that the lengths of all strings used in a particular cover satisfy $ N \le n < N/\theta + 1$, where $ \theta \in [0,1]$ is a parameter. When $ \theta = 1$, only covers using strings of the same length are allowed, and we recover the lower and upper capacity topological entropies; when $ \theta = 0$, there are no restrictions, and the definition coincides with the topological entropy. We first establish a quantitative inequality for the upper and lower intermediate topological entropies, which mirrors the corresponding result for intermediate dimensions. As a consequence, the intermediate topological entropies are continuous on $(0,1]$, though discontinuity may arise at $0$; an illustrative example is provided to demonstrate this phenomenon. We then investigate several fundamental properties of the intermediate topological entropies for nonautonomous dynamical systems, including the power rule, monotonicity and product formulas. Finally, we derive an inequality relating intermediate entropies with respect to factor maps.

math.DS↗