ROTH, Samuel Joshua and Zuzana ROTH. Inequalities for entropy, Hausdorff dimension, and Lipschitz constants. Studia Mathematica. WARSZAWA: POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN, 2020, vol. 250, No 3, p. 253-264. ISSN 0039-3223. Available from: https://dx.doi.org/10.4064/sm180705-2-11. |
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@article{49267, author = {Roth, Samuel Joshua and Roth, Zuzana}, article_location = {WARSZAWA}, article_number = {3}, doi = {http://dx.doi.org/10.4064/sm180705-2-11}, keywords = {topological entropy; Hausdorff dimension; Lipschitz continuity}, language = {eng}, issn = {0039-3223}, journal = {Studia Mathematica}, title = {Inequalities for entropy, Hausdorff dimension, and Lipschitz constants}, url = {https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/250/3/113169/inequalities-for-entropy-hausdorff-dimension-and-lipschitz-constants}, volume = {250}, year = {2020} }
TY - JOUR ID - 49267 AU - Roth, Samuel Joshua - Roth, Zuzana PY - 2020 TI - Inequalities for entropy, Hausdorff dimension, and Lipschitz constants JF - Studia Mathematica VL - 250 IS - 3 SP - 253-264 EP - 253-264 PB - POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN SN - 00393223 KW - topological entropy KW - Hausdorff dimension KW - Lipschitz continuity UR - https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/250/3/113169/inequalities-for-entropy-hausdorff-dimension-and-lipschitz-constants N2 - We construct suitable metrics for two classes of topological dynamical systems (linear maps on the torus and non-invertible expansive maps on compact spaces) in order to get a lower bound for topological entropy in terms of the resulting Hausdorff dimensions and Lipschitz constants. This reverses an old inequality of Dai, Zhou, and Geng and leads to a short proof of a well-known theorem on expansive mappings. It also suggests a new invariant of topological conjugacy for dynamical systems on compact metric spaces. ER -
ROTH, Samuel Joshua and Zuzana ROTH. Inequalities for entropy, Hausdorff dimension, and Lipschitz constants. \textit{Studia Mathematica}. WARSZAWA: POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN, 2020, vol.~250, No~3, p.~253-264. ISSN~0039-3223. Available from: https://dx.doi.org/10.4064/sm180705-2-11.
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