We compute the Hausdorff dimension of the “multiplicative golden mean shift” defined as the set of all reals in whose binary expansion satisfies for all , and show that it is smaller than the Minkowski dimension.
Nous calculons la dimension de Hausdorff du « shift de Fibonacci multiplicatif », cʼest-à-dire lʼensemble des nombres réels dans dont le développement en binaire satisfait pour tout . Nous montrons que la dimension de Hausdorff est plus petite que la dimension de Minkowski.
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Richard Kenyon 1; Yuval Peres 2; Boris Solomyak 3
@article{CRMATH_2011__349_11-12_625_0, author = {Richard Kenyon and Yuval Peres and Boris Solomyak}, title = {Hausdorff dimension of the multiplicative golden mean shift}, journal = {Comptes Rendus. Math\'ematique}, pages = {625--628}, publisher = {Elsevier}, volume = {349}, number = {11-12}, year = {2011}, doi = {10.1016/j.crma.2011.05.009}, language = {en}, }
TY - JOUR AU - Richard Kenyon AU - Yuval Peres AU - Boris Solomyak TI - Hausdorff dimension of the multiplicative golden mean shift JO - Comptes Rendus. Mathématique PY - 2011 SP - 625 EP - 628 VL - 349 IS - 11-12 PB - Elsevier DO - 10.1016/j.crma.2011.05.009 LA - en ID - CRMATH_2011__349_11-12_625_0 ER -
Richard Kenyon; Yuval Peres; Boris Solomyak. Hausdorff dimension of the multiplicative golden mean shift. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 625-628. doi : 10.1016/j.crma.2011.05.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.05.009/
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