Denseness of intermediate pressures for systems with the Climenhaga-Thompson structures. (English) Zbl 1439.37042
Summary: We show that systems with the structure introduced by V. Climenhaga and D. J. Thompson [Isr. J. Math. 192, Part B, 785–817 (2012; Zbl 1279.37011); Ergodic Theory Dyn. Syst. 34, No. 6, 1816–1831 (2014; Zbl 1322.37015); Adv. Math. 303, 745–799 (2016; Zbl 1366.37084)]
have dense intermediate pressures and dense intermediate entropies of ergodic measures. The result applies to the Mañé diffeomorphisms.
MSC:
| 37D35 | Thermodynamic formalism, variational principles, equilibrium states for dynamical systems |
| 37C40 | Smooth ergodic theory, invariant measures for smooth dynamical systems |
| 37D25 | Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) |
| 37D30 | Partially hyperbolic systems and dominated splittings |
| 37C05 | Dynamical systems involving smooth mappings and diffeomorphisms |
Keywords:
ergodic measure; intermediate entropy; pressure; specification; Climenhaga-Thompson structure; Mañé diffeomorphismReferences:
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