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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2014

On the dynamics of a family of generated renormalization transformations

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Fei Yang
  • Fonction : Auteur
  • PersonId : 766331
  • IdRef : 161502865
Jinsong Zeng
  • Fonction : Auteur
  • PersonId : 1084183

Résumé

We study the family of renormalization transformations of the generalized d  -dimensional diamond hierarchical Potts model in statistical mechanic and prove that their Julia sets and non-escaping loci are always connected, where d⩾2. In particular, we prove that their Julia sets can never be a Sierpiński carpet if the parameter is real. We show that the Julia set is a quasicircle if and only if the parameter lies in the unbounded capture domain of these models. Moreover, the asymptotic formula of the Hausdorff dimension of the Julia set is calculated as the parameter tends to infinity.

Dates et versions

hal-03038377 , version 1 (03-12-2020)

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Citer

Fei Yang, Jinsong Zeng. On the dynamics of a family of generated renormalization transformations. Journal of Mathematical Analysis and Applications, 2014, 413 (1), pp.361-377. ⟨10.1016/j.jmaa.2013.11.068⟩. ⟨hal-03038377⟩
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