A thermodynamic classification of real numbers

JOURNAL OF NUMBER THEORY

卷:130

Article

Garrity, Thomas

关键词: Diophantine approximations;    Continued fractions;    Thermodynamic formalism;   

DOI  :  10.1016/j.jnt.2010.01.016

来源: Elsevier

【 摘 要 】

Text. A new classification scheme for real numbers is given, motivated by ideas from statistical mechanics in general and work of Knauf (1993) [16] and Fiala and Kleban (2005) [8] in particular. Critical for this classification of a real number will be the Diophantine properties of its continued fraction expansion. Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=onPF2QS4cRg. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free