ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




Free energies as invariants of Teichmüller like structures

A. Mesón and F. Vericat

Received: December 21, 2010;   Revised: October 22, 2012;   Accepted: October 23, 2012



Abstract.   A Teichmüller like structure on the space of d-degree holomorphic maps on the circle S1, marked by conjugations to the map z ® zd, can be defined. Here we introduce a definition of free energy associated to this kind of dynamics as an invariant of equivalence classes in the Teichmüller space. This quantity encodes a length spectrum of rotation cycles in S1.

Keywords:  Free energy; circle map; Teichmüller space.  

AMS Subject classification: Primary:  37E10,37F30  


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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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