On the variational principle for the topological entropy of certain non-compact sets

By Floris Takens, Evgeny A. Verbitskiy. Ergodic Theory and Dynamical Systems, 2003

184 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d183114431193d7c01779b2f583cb129a142e8bc

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In Computer Networks and Communications

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Citations in the corpus

Wavelets on Fractals (2003, background): “The practical applications are to fractals arising in physics and in symbolic dynamical systems from theoretical computer science, see e.g., [4] [17], [ 24 ].”
The irregular set for maps with the specification property has full topological pressure (2008, methodology): “We adapt an ingenious method of Takens and Verbitskiy, which can be found in Section 5 of [11] and was in turn developed from a large deviations proof of Young [21].”
Multifractal analysis of non-uniformly hyperbolic systems (2008, background): “In the case of general continuous functions there are results for topological entropy [13], but not for Hausdorff dimension.”
Distribution of frequencies of digits via multifractal analysis (2002, background): “The following is an immediate consequence of work of Takens and Verbitskiy [ 13 ], where we make the convention that sup ? = 0. Theorem 10. Let : [0; 1] ! U Rr and : U ! Rp be piecewise continuous functions with nitely many discontinuities and at most at negative powers of m. For each 2 Rp we have”
Rotation, entropy, and equilibrium states (2001, background): “I thank Evgeny Verbitski for pointing out an error in a previous version of this paper, and for a copy of [52].”
A variational principle for topological pressure for certain non‐compact sets (2008, methodology): “The following lemma (the proof is included for completeness) is essentially contained in [19].”
Higher-dimensional multifractal analysis (2002, background): “Takens and Verbitskiy recently observed in [14] that their statement also holds when Ψ = (1, .”
A PANORAMA OF SPECIFICATION-LIKE PROPERTIES AND THEIR CONSEQUENCES (2015, methodology): “The specification property was used by Takens and Verbitskiy [85] to obtain a variational description of the dimension of multifractal decompositions.”
The Lyapunov spectrum of some parabolic systems (2007, methodology): “For such a system, the vanishing of the entropy htop(f |L(0)) as stated below follows in fact from [ 15, Theorem 3.5 ] and the Ruelle inequality.”
On the topological entropy of saturated sets (2007, methodology): “Proposition 7.1 is the main result in [ TV ].”
Large deviations estimates for dynamical systems without the specification property. Application to the β-shifts (2005, methodology): “Remark. Results of this kind have been obtained by Tempelman [Te2] and Takens and Verbitskiy [ TV2 ].”
Variational principles and mixed multifractal spectra (2001, background): “Verbitski [ 11 ] under the assumption that f is a continuous transformation satisfying specication, and ’ is an arbitrary continuous function (and thus may have more than one equilibrium measure), with a very dieren t approach.”
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 ].”
Lyapunov Spectrum of Asymptotically Sub-additive Potentials (2009, background): “TDS satisfying the specication property [ 46 ].”