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Beta-shifts without typical periodic optimization
Wen Huang, Oliver Jenkinson, Leiye Xu +1
We show that beta-shifts whose lexicographically largest point is a Sturmian sequence do not have typical periodic optimization (TPO): on each such beta-shift there is a non-empty…
Typical periodic optimization for dynamical systems: symbolic dynamics
Wen Huang, Oliver Jenkinson, Leiye Xu +1
We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Mañé cohomology lemma does n…
Typical Uniqueness in Ergodic Optimization
Oliver Jenkinson, Xiaoran Li, Yuexin Liao +1
For ergodic optimization on any topological dynamical system, with real-valued potential function belonging to any separable Banach space of continuous functions, we show t…
Ergodic Optimization for Open Expanding Multi-valued Topological Dynamical Systems
Oliver Jenkinson, Xiaoran Li, Yuexin Liao +1
We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumpti…