The entropy of Nakada's α-continued fractions: analytical results

• Giulio Tiozzo ^[1]
  1. [1] Yale University

     Yale University

     Town of New Haven, Estados Unidos

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 4, 2014, págs. 1009-1037
• Idioma: inglés
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• Resumen

  • We study the ergodic theory of a one-parameter family of interval maps Tα arising from generalized continued fraction algorithms. First of all, we prove the dependence of the metric entropy of Tα to be H¨older-continuous in the parameter α. Moreover, we prove a central limit theorem for possibly unbounded observables whose bounded variation grows moderately. This class of functions is large enough to cover the case of Birkhoff averages converging to the entropy.