Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Computability of the Julia set. Nonrecurrent critical orbits

Pages: 2751 - 2778, Volume 34, Issue 7, July 2014      doi:10.3934/dcds.2014.34.2751

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Artem Dudko - Institute for Mathematical Sciences, Stony Brook University, Stony Brook, NY, 11794-3660, United States (email)

Abstract: We prove, that the Julia set of a rational function $f$ is computable in polynomial time, assuming that the postcritical set of $f$ does not contain any critical points or parabolic periodic orbits.

Keywords:  Computability, computational complexity, Julia set.
Mathematics Subject Classification:  Primary: 37F50, 37F10; Secondary: 03F60.

Received: June 2012;      Revised: September 2013;      Available Online: December 2013.