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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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