Variational principle for unstable packing topological entropy
Fixed Point Methods and Optimization, Volume 2, Issue 2, August 2025, Pages 149–157
TIANKUI LUO
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, China 400074
CHENSHI ZHOU
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, China 400074
WENDA ZHANG
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, China 400074
Abstract
In this paper we define unstable packing topological entropy \(h_{p}^{u}(f,Z)\) for any subsets (not necessarily compact or invariant) in partially hyperbolic dynamical systems as a packing dimension characteristic, and the unstable measure theoretical upper entropy \(\overline{h}^{u}_{\mu}(f)\) for any \(\mu\in\mathcal{M}(M)\), where \(\mathcal{M}(M)\) denotes the collection of all Borel probability measures on \(M\). For any non-empty compact subset \(Z\subseteq M\), we will prove a variational principle for unstable packing topological entropy: for any Borel subset \(Z\) of \(M\), the unstable packing topological entropy of \(Z\) equals the supremum of unstable measure theoretical upper entropy over all Borel probability measures for which the subset \(Z\) has full measure.
Cite this Article as
Tiankui Luo, Chenshi Zhou and Wenda Zhang, Variational principle for unstable packing topological entropy, Fixed Point Methods and Optimization, 2(2), 149–157, 2025