Smooth interval maps have symbolic extensions

DOI10.1007/s00222-008-0172-4zbMath1185.37100OpenAlexW2050514343MaRDI QIDQ1030525

Tomasz Downarowicz, Alejandro Maass

Publication date: 1 July 2009

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-008-0172-4

zbMATH Keywords

entropysymbolic dynamicsone dimensional dynamicsdifferentiable dynamics

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Dynamical systems involving maps of the interval (37E05)

Related Items (12)

Asymptotich-expansiveness rate ofC^∞maps ⋮ Jumps of entropy for C^rinterval maps ⋮ Weak expansion properties and large deviation principles for expanding Thurston maps ⋮ Orders of accumulation of entropy on manifolds ⋮ Symbolic extensions and dominated splittings for generic \(C^1\)-diffeomorphisms ⋮ \(\mathcal{C}^{2}\) surface diffeomorphisms have symbolic extensions ⋮ Existence of measures of maximal entropy for 𝒞^{𝓇} interval maps ⋮ Symbolic extensions and continuity properties of the entropy ⋮ Periodic points and measures for a class of skew-products ⋮ Symbolic extensions for 3-dimensional diffeomorphisms ⋮ The symbolic extension theory in topological dynamics ⋮ Symbolic Extensions of Amenable Group Actions and the Comparison Property

Cites Work

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• A direct proof of the tail variational principle and its extension to maps
• Topological conditional entropy
• Hyperbolic sets exhibiting $C^1$-persistent homoclinic tangency for higher dimensions
• Lectures on Choquet's theorem

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