Intrinsic ergodicity of smooth interval maps
From MaRDI portal
Publication:1366943
DOI10.1007/BF02773637zbMath0889.28009OpenAlexW2078794687MaRDI QIDQ1366943
Publication date: 23 June 1998
Published in: Israel Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02773637
critical pointslocal entropyintrinsic ergodicitysmooth interval mapergodic measures of maximal entropy
Measure-preserving transformations (28D05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) General groups of measure-preserving transformations (28D15) Ergodic theory (37A99)
Related Items (73)
Dimensions of stable sets and scrambled sets in positive finite entropy systems ⋮ A convex analysis approach to entropy functions, variational principles and equilibrium states ⋮ Intrinsic ergodicity of affine maps in \([0,1^ d\)] ⋮ Dynamics in dimension zero A survey ⋮ A lower bound for topological entropy of generic non-Anosov symplectic diffeomorphisms ⋮ The entropy of 𝐶¹-diffeomorphisms without a dominated splitting ⋮ surface diffeomorphisms with no maximal entropy measure ⋮ Intrinsic ergodicity via obstruction entropies ⋮ Isomorphism and embedding of Borel systems on full sets ⋮ Asymptotich-expansiveness rate ofC∞maps ⋮ Symbolic dynamics for one dimensional maps with nonuniform expansion ⋮ Jumps of entropy for Crinterval maps ⋮ The entropy conjecture for diffeomorphisms away from tangencies ⋮ Weak expansion properties and large deviation principles for expanding Thurston maps ⋮ Countably and entropy expansive homeomorphisms with the shadowing property ⋮ A local conditional variational principle of pressures and local conditional equilibrium states ⋮ Sub-additive topological and measure-theoretic tail pressures ⋮ Effective intrinsic ergodicity for countable state Markov shifts ⋮ Uniform generators, symbolic extensions with an embedding, and structure of periodic orbits ⋮ Natural extensions for piecewise affine maps via Hofbauer towers ⋮ Intrinsic ergodicity beyond specification: \({\beta}\)-shifts, \(S\)-gap shifts, and their factors ⋮ Orders of accumulation of entropy on manifolds ⋮ Tail variational principle and asymptotic \(h\)-expansiveness for amenable group actions ⋮ Nonlinear thermodynamical formalism ⋮ Symbolic extensions and dominated splittings for generic \(C^1\)-diffeomorphisms ⋮ Measures of intermediate entropies and homogeneous dynamics ⋮ Topological conjugacy on the complement of the periodic points ⋮ Markov diagrams for some non-Markovian systems ⋮ \(\mathcal{C}^{2}\) surface diffeomorphisms have symbolic extensions ⋮ On Omri Sarig's work on the dynamics on surfaces ⋮ Topological and Measure-Theoretical Entropies of a Solenoid ⋮ Generic continuity of metric entropy for volume-preserving diffeomorphisms ⋮ Tail variational principle for a countable discrete amenable group action ⋮ Existence of measures of maximal entropy for 𝒞^{𝓇} interval maps ⋮ Continuity of topological entropy for perturbation of time-one maps of hyperbolic flows ⋮ Phase transitions for the geodesic flow of a rank one surface with nonpositive curvature ⋮ Uniform tail entropy for real analytic maps ⋮ A local variational principle of pressure and its applications to equilibrium states ⋮ Symbolic dynamics for surface diffeomorphisms with positive entropy ⋮ Subshifts of quasi-finite type ⋮ Lyapunov spectrum of asymptotically sub-additive potentials ⋮ Puzzles of quasi-finite type, zeta functions and symbolic dynamics for multi-dimensional maps ⋮ Lowering topological entropy over subsets ⋮ Symbolic extensions and smooth dynamical systems ⋮ The work of Mike Hochman on multidimensional symbolic dynamics and Borel dynamics ⋮ Entropy conjugacy for Markov multi-maps of the interval ⋮ Uniqueness of the measure of maximal entropy for the standard map ⋮ Beyond topological hyperbolicity: the L-shadowing property ⋮ A proof of Yomdin-Gromov's algebraic Lemma ⋮ Entropy of partially hyperbolic flows with center dimension two ⋮ Stable sets and \(\epsilon\)-stable sets in positive-entropy systems ⋮ A direct proof of the tail variational principle and its extension to maps ⋮ Ergodic measures of intermediate entropy for affine transformations of nilmanifolds ⋮ Almost isomorphism for countable state Markov shifts ⋮ Markov extensions for multi-dimensional dynamical systems ⋮ Entropies for Negatively Curved Manifolds ⋮ 𝐶ⁿ interval maps not Borel conjugate to any 𝐶^{∞} map ⋮ Tail entropy and hyperbolicity of measures ⋮ Periodic points and measures for a class of skew-products ⋮ Smooth interval maps have symbolic extensions ⋮ Maximal entropy measures for piecewise affine surface homeomorphisms ⋮ Symbolic extensions for 3-dimensional diffeomorphisms ⋮ Complex cellular structures ⋮ The symbolic extension theory in topological dynamics ⋮ Maximal entropy measures of diffeomorphisms of circle fiber bundles ⋮ Measures of maximal entropy for surface diffeomorphisms ⋮ Continuity properties of Lyapunov exponents for surface diffeomorphisms ⋮ Bowen’s entropy-conjugacy conjecture is true up to finite index ⋮ Statistical properties of physical-like measures* ⋮ Ergodicité intrinsèque de produits fibrés d'applications chaotiques unidimensionnelles ⋮ On the continuity of topological entropy of certain partially hyperbolic diffeomorphisms ⋮ Entropy structure ⋮ Mixing \(C^r\) maps of the interval without maximal measure.
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Volume growth and entropy
- \(C^ k\)-resolution of semialgebraic mappings, addendum to volume growth and entropy
- Continuity properties of entropy
- On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
- Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
- Ergodic theory on compact spaces
- Intrinsic ergodicity of affine maps in \([0,1^ d\)]
- Ergodic properties of nonnegative matrices. I
- Decomposition of dynamical systems on an interval
- GEOMETRIC ERGODICITY IN DENUMERABLE MARKOV CHAINS
- The structure of piecewise monotonic transformations
- Number of Equilibrium States of Piecewise Monotonic Maps of the Interval
- Entropy for Group Endomorphisms and Homogeneous Spaces
- Intrinsically ergodic systems
- Entropy-Expansive Maps
This page was built for publication: Intrinsic ergodicity of smooth interval maps