Analytic families of semihyperbolic generalized polynomial-like mappings

作者：Urbanski Mariusz^*

来源：Monatshefte fur Mathematik, 2010, 159(1-2): 133-162.

DOI：10.1007/s00605-008-0081-z

• Holomorphic dynamics
• Hausdorff dimension
• Semihyperbolic generalized polynomial-like mappings
• Real analyticity
• Julia sets
• Conformal graph directed Markov systems

We show that the Hausdorff dimension of Julia sets in any analytic family of semihyperbolic generalized polynomial-like mappings (GPL) depends in a real-analytic manner on the parameter. For the proof we introduce abstract weakly regular analytic families of conformal graph directed Markov systems. We show that the Hausdorff dimension of limit sets in such families is real-analytic, and we associate to each analytic family of semihyperbolic GPLs a weakly regular analytic family of conformal graph directed Markov systems with the Hausdorff dimension of the limit sets equal to the Hausdorff dimension of the Julia sets of the corresponding semihyperbolic GPLs.

• 出版日期2010-1