Thermodynamic formalism and circle homeophormisms with a break-type singularity

A renormalization group (RG) transformation on the space of circle homeomorphisms with break-type singularity point and with the rotation number \rho =\genfrac{\sqrt{5}-1}{2} (``golden mean'') has a unique periodic trajectory $\{T_{1},T_{2}\}$ with period two. For homeomorphisms $T$ which are $C^{1}-$conjugate to $T_{1}$ $($ or $T_{2})$ the behavior of Holder's exponents of singular invariant measure are studied. Limit distributions of entrance times are also studied

Thermodynamic formalism and circle homeomorphisms with a break-type singularity

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 , Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal