A new proof of the dimension gap for the Gauss map
Abstract
In [4], Kifer, Peres and Weiss showed that the Bernoulli measures for the Gauss map T(x)=1/x mod 1 satisfy a 'dimension gap' meaning that for some c > 0, supp dim μp < 1-c, where μp denotes the (pushforward) Bernoulli measure for the countable probability vector p. In this paper we propose a new proof of the dimension gap. By using tools from thermodynamic formalism we show that the problem reduces to obtaining uniform lower bounds on the asymptotic variance of a class of potentials.
Citation
Jurga , N 2021 , ' A new proof of the dimension gap for the Gauss map ' , Mathematical Proceedings of the Cambridge Philosophical Society , vol. FirstView . https://doi.org/10.1017/S0305004121000104
Publication
Mathematical Proceedings of the Cambridge Philosophical Society
Status
Peer reviewed
ISSN
0305-0041Type
Journal article
Description
Funding: This paper was written while the author was supported by a Leverhulme Trust Research Project Grant (RF-2016-194).Collections
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