p. 1 - 10 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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2013, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |