Advanced Search
Article Contents
Article Contents

Hermodynamic formalism and k-bonacci substitutions

Abstract Full Text(HTML) Related Papers Cited by
  • We study k-bonacci substitutions through the point of view of thermodynamic formalism. For each substitution we define a renormalization operator associated to it and examine its iterates over potentials in a certain class. We also study the pressure function associated to potentials in this class and prove the existence of a freezing phase transition which is realized by the only ergodic measure on the subshift associated to the substitution.

    Mathematics Subject Classification: Primary: 37D35, 37B10; Secondary: 37C30.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] P. Arnoux and G. Rauzy, Représentation géométrique de suites de complexité 2n + 1, Bull. Soc. Math. France, 119 (1991), 199-215. 
    [2] A. BaravieraR. Leplaideur and A. Lopes, The potential point of view for renormalization, Stoch. Dyn., 12 (2012), 1250005, 34pp.  doi: 10.1142/S0219493712500050.
    [3] N. Bédaride, P. Hubert and R. Leplaideur, Thermodynamic formalism and substitutions, Preprint, arXiv: 1511.03322.
    [4] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, revised edition, Springer-Verlag, Berlin, 2008.
    [5] H. Bruin and R. Leplaideur, Renormalization, thermodynamic formalism and quasi-crystals in subshifts, Comm. Math. Phys., 321 (2013), 209-247.  doi: 10.1007/s00220-012-1651-4.
    [6] H. Bruin and R. Leplaideur, Renormalization, freezing phase transitions and Fibonacci quasicrystals, Ann. Sci. éc. Norm. Supér., 48 (2015), 739-763. 
    [7] J. Cassaigne, Complexité et facteurs spéciaux, Bull. Belg. Math. Soc. Simon Stevin, 4 (1997), 67-88. 
    [8] D. Coronel and J. Rivera-Letelier, Low-temperature phase transitions in the quadratic family, Adv. Math., 248 (2013), 453-494.  doi: 10.1016/j.aim.2013.08.008.
    [9] F. Durand, Linearly recurrent subshifts have a finite number of non-periodic subshift factors, Ergodic Theory Dynam. Systems, 20 (2000), 1061-1078.  doi: 10.1017/S0143385700000584.
    [10] B. Mossé, Puissances de mots et reconnaissabilité des points fixes d'une substitution, Theoret. Comput. Sci., 99 (1992), 327-334.  doi: 10.1016/0304-3975(92)90357-L.
    [11] M. QueffélecSubstitution Dynamical Systems -Spectral Analysis, Lecture Notes in Mathematics, Springer Berlin Heidelberg, (2010).  doi: 10.1007/978-3-642-11212-6.
    [12] G. Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France, 110 (1982), 147-178. 
    [13] D. RuelleThermodynamic Formalism. second edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2004.  doi: 10.1017/CBO9780511617546.
    [14] O. Sarig, Phase transitions for countable Markov shifts, Comm. Math. Phys., 217 (2001), 555-577.  doi: 10.1007/s002200100367.
  • 加载中

Article Metrics

HTML views(501) PDF downloads(51) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint