論文

査読有り
2014年8月

Multifractal formalism for Benedicks-Carleson quadratic maps

ERGODIC THEORY AND DYNAMICAL SYSTEMS
  • Yong Moo Chung
  • ,
  • Hiroki Takahasi

34
開始ページ
1116
終了ページ
1141
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1017/etds.2012.188
出版者・発行元
CAMBRIDGE UNIV PRESS

For a positive measure set of non-uniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given continuous function and consider the associated Birkhoff spectrum which encodes this decomposition. We derive a formula which relates the Hausdorff dimension of level sets to entropies and Lyapunov exponents of invariant probability measures, and then use this formula to show that the spectrum is continuous. In order to estimate the Hausdorff dimension from above, one has to 'see' sufficiently many points. To this end, we construct a family of towers. Using these towers we establish a large deviation principle of empirical distributions, with Lebesgue as a reference measure.

Web of Science ® 被引用回数 : 8

リンク情報
DOI
https://doi.org/10.1017/etds.2012.188
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000341845700004&DestApp=WOS_CPL

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