Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension

By Luís Barreira, J. Schmeling. 2000

382 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a99b74629ba1db5a5e790a22d41d6f611b0cf542

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In Computational Theory and Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Variational principles for topological entropies of subsets (2010, neutral): “[2]).”
Multifractal Analysis of Hyperbolic Flows (2000, methodology): “In [ 3 ], Barreira and Schmeling studied irregular sets with respect to dieomorphisms on hyperbolic sets.”
On the topological entropy of saturated sets (2007, background): “Another important related work is Barreira and Schmeling’s paper [ BaSc ] about Hausdorff dimension and topological entropy of sets of “non-typical” points.”
Irregular sets, the -transformation and the almost specification property (2012, positive): “Symbolic dynamics methods have confirmed this in the uniformly hyperbolic setting [3], for certain non-uniformly hyperbolic examples [23] and for a large class of multimodal maps [31].”
Normal and Non‐Normal Points of Self‐Similar Sets and Divergence Points of Self‐Similar Measures (2003, background): “Divergence points of self-similar measures Recently Barreira and Schmeling [2] and Chen and Xiong [4] have shown that the set of divergence points not considered by the multifractal spectra functions in Theorem A, that is, the set D = K \⋃ α π { ω ∈ Σ ∣∣∣∣ limn log µKω|nlog diamKω|n = α } = π { ω ∈ ”
Almost additive multifractal analysis (2009, neutral): “2 in [6] that dimuI min { dimuμ ,dimuμ 1, .”
Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices (2003, background): “Theorem A extends the corresponding results for the Birkho averages of scalar functions, for which one is referred to, e.g., [1, 2, 3 , 9, 10, 16, 35, 38, 40, 41, 47].”
Pointwise dimensions for Poincaré recurrences associated with maps and special flows (2002, background): “As it was shown in [6], the remaining zero set can be very large in terms of topological entropy or dimension.”