Dimension de Hausdorff du shift de Fibonacci multiplicatif

Richard Kenyon; Yuval Peres; Boris Solomyak

doi:10.1016/j.crma.2011.05.009

Dimension de Hausdorff du shift de Fibonacci multiplicatif

Translated title of the contribution: Hausdorff dimension of the multiplicative golden mean shift

Richard Kenyon
, Yuval Peres
, Boris Solomyak

Research output: Contribution to journal › Article › peer-review

Abstract

We compute the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in [0,1] whose binary expansion (xk) satisfies xkx2k=0 for all k≥1, and show that it is smaller than the Minkowski dimension. 2011 Académie des sciences.

Translated title of the contribution	Hausdorff dimension of the multiplicative golden mean shift
Original language	French
Pages (from-to)	625-628
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	349
Issue number	11-12
DOIs	https://doi.org/10.1016/j.crma.2011.05.009
State	Published - Jun 2011
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2011.05.009

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title = "Dimension de Hausdorff du shift de Fibonacci multiplicatif",

abstract = "We compute the Hausdorff dimension of the {"}multiplicative golden mean shift{"} defined as the set of all reals in [0,1] whose binary expansion (xk) satisfies xkx2k=0 for all k≥1, and show that it is smaller than the Minkowski dimension. 2011 Acad{\'e}mie des sciences.",

author = "Richard Kenyon and Yuval Peres and Boris Solomyak",

note = "Funding Information: We are grateful to J{\"o}rg Schmeling for telling us about the problem, and to Aihua Fan, Lingmin Liao, and Jihua Ma for sending us their preprint [4] prior to publication. The research of R.K. and B.S. was supported in part by NSF.",

year = "2011",

month = jun,

doi = "10.1016/j.crma.2011.05.009",

language = "الفرنسيّة",

volume = "349",

pages = "625--628",

journal = "Comptes Rendus Mathematique",

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publisher = "Academie des sciences",

number = "11-12",

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T1 - Dimension de Hausdorff du shift de Fibonacci multiplicatif

AU - Kenyon, Richard

AU - Peres, Yuval

AU - Solomyak, Boris

N1 - Funding Information: We are grateful to Jörg Schmeling for telling us about the problem, and to Aihua Fan, Lingmin Liao, and Jihua Ma for sending us their preprint [4] prior to publication. The research of R.K. and B.S. was supported in part by NSF.

PY - 2011/6

Y1 - 2011/6

N2 - We compute the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in [0,1] whose binary expansion (xk) satisfies xkx2k=0 for all k≥1, and show that it is smaller than the Minkowski dimension. 2011 Académie des sciences.

AB - We compute the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in [0,1] whose binary expansion (xk) satisfies xkx2k=0 for all k≥1, and show that it is smaller than the Minkowski dimension. 2011 Académie des sciences.

UR - https://www.scopus.com/pages/publications/79959563976

U2 - 10.1016/j.crma.2011.05.009

DO - 10.1016/j.crma.2011.05.009

M3 - مقالة

SN - 1631-073X

VL - 349

SP - 625

EP - 628

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 11-12

ER -

Dimension de Hausdorff du shift de Fibonacci multiplicatif

Abstract

ASJC Scopus subject areas

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