Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:A1L-B

Session:

Number:2

Computability and Complexity of Julia Sets

Kota Hiratsuka,  Yuzuru Sato,  Zin Arai,  

pp.2-5

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.2

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Since A. M. Turing introduced a notion of computability, various types of real number computation theory has been studied for past 80 years [1-6]. Some of them are of interest in nonlinear and statistical physics, and others are as extensions of mathematical theory of computation. In this review paper, we introduce recently developed computability theory of Julia sets in the framework of M. Braverman and M. Yampolsky [7], and give remarks and future works.

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[4] J. Crutchfield, K. Young, “Inferring statistical complexity,” Phys. Rev. Lett., 63,p105-108, (1989).

[5] K. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, (1991).

[6] L. Blum, F. Cucker, M. Shub and S. Smale, “Complexity and Real Computation”; Springer-Verlag / Berlin, (1998).

[7] M. Braverman, and M. Yampolsky, “Computability of Julia sets,” Springer-Verlag / Berlin, (2009).

[8] J. Milnor, “Dynamics in one complex variable Third Edition”, Princeton University Press, (2006).