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We give a lower bound of the hyperbolic and the Hausdorff dimension of the Julia set of meromorphic functions of finite order under very general conditions.

In this paper we investigate the dynamics of certain rational functions on their Julia sets. We pay particular attention to the case where the Julia set is a Sierpinski curve. In this case, any two such Julia sets are known to be homeomorphic. However, the dynamics on these sets are often quite different. In this paper, we use symbolic dynamics to show how these different dynamical behaviors ma...

We study a class of functions A given by Epstein in Towers of finite type complex analytic maps, ProQuest LLC, Ann Arbor, MI, 1993, called finite-type maps. We extend a result related with the Julia set given by Baker, Domı́nguez in Some connectedness properties of Julia sets, Complex Variable Theory Appl. 41 (2000), 371–389, and Baker, Domı́nguez, and Herring in Dynamics of functions meromorphic...

We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.

There exist uniformly quasiregular maps f : R → R whose Julia sets are wild Cantor sets.

Presented is a Julia meta-program that discovers compact theories from data if they exist. It writes candidate theories in Julia and then validates: tossing the bad theories and keeping the good theories. Compactness is measured by a metric: such as the number of space-time derivatives. The underlying algorithm is applicable to a wide variety of combinatorics problems and compactness serves to ...

Xiaoyue Ni, Stefanos Papanikolaou, 3, 4 Gabriele Vajente, Rana X Adhikari, and Julia R. Greer Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91125 Department of Mechanical Engineering, Johns Hopkins University, 3400 N Charles St, Baltimore, MD 21218. Department of Mechanical and Aerospace Engineering, West Virginia University, 395 Evansdale Dr, Mo...