A natural space of functions for the Ruelle operator theorem

• Autores: Peter Walters
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 4, 2007, págs. 1323-1348
• Idioma: inglés
• DOI: 10.1017/s0143385707000028
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study a new space, $R(X)$, of real-valued continuous functions on the space $X$ of sequences of zeros and ones. We show exactly when the Ruelle operator theorem holds for such functions. Any $g$-function in $R(X)$ has a unique $g$-measure and powers of the corresponding transfer operator converge. We also show Bow$(X,T)\neq W(X,T)$ and relate this to the existence of bounded measurable coboundaries, which are not continuous coboundaries, for the shift on the space of bi-sequences of zeros and ones.