Twelve open problems on the exact value of the Hausdorff measure and on topological entropy: a brief survey of recent results
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Publication:4810804
DOI10.1088/0951-7715/17/2/007zbMath1047.28002OpenAlexW2040162086MaRDI QIDQ4810804
Publication date: 16 August 2004
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0951-7715/17/2/007
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HAUSDORFF MEASURE OF CARTESIAN PRODUCT OF THE TERNARY CANTOR SET ⋮ Recurrence of transitive points in dynamical systems with the specification property ⋮ Irregular recurrence in compact metric spaces ⋮ Distributional chaos and irregular recurrence ⋮ Continuity of packing measure functions of self-similar iterated function systems ⋮ An algorithm for computing the centered Hausdorff measures of self-similar sets ⋮ Weakly controlled Moran constructions and iterated functions systems in metric spaces ⋮ Continuous maps that preserve Hausdorff measure ⋮ On quasi-weakly almost periodic points ⋮ The upper capacity topological entropy of free semigroup actions for certain non-compact sets ⋮ An equivalent condition for the self similar sets on the real line to have best coverings ⋮ Some results on the upper convex densities for the self-similar sets ⋮ An answer to a conjecture on self-similar sets ⋮ Different asymptotic behavior versus same dynamical complexity: recurrence \& (ir)regularity ⋮ Elementary density bounds for self-similar sets and application ⋮ Weakly Birkhoff recurrent switching signals, almost sure and partial stability of linear switched dynamical systems ⋮ The upper capacity topological entropy of free semigroup actions for certain non-compact sets. II ⋮ Transitively-saturated property, Banach recurrence and Lyapunov regularity ⋮ On the exact Hausdorff measure of a class of self-similar sets satisfying open set condition ⋮ Distributional chaos in multifractal analysis, recurrence and transitivity ⋮ An equivalent condition for the full Hausdorff measure of a subset of the set of finite type ⋮ On quasi-weakly almost periodic points of continuous flows ⋮ The minimum of the upper convex density of the product of the Cantor set with itself ⋮ Exact Hausdorff and packing measures of Cantor sets with overlaps ⋮ An isodiametric problem with additional constraints ⋮ Inducing Sensitivity of Fuzzified Dynamical Systems ⋮ Self-similar sets with optimal coverings and packings ⋮ Hausdorff measure of uniform self-similar fractals ⋮ A negative answer to a conjecture on self-similar sets with open set condition ⋮ Some problems on fractal geometry and topological dynamical systems ⋮ Connecting Hausdorff measure and upper convex density or \(H^s\)-a.e. covering ⋮ A note on quasi-weakly almost periodic point
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