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The polynomial topological complexity of Fatou-Julia sets

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Abstract

We analyze the polynomial topological complexity of Fatou-Julia sets, and show that for Sullivan domains of such sets the complexity is equal to 1 in the case of attracting, superattracting and Siegel domains, while for parabolic domains it is greater than 1.

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References

  1. Baker and Eremenko, A problem on Julia sets, Ann. Acad. Sci. Fenn. 12 (1987) 229–236.

    MATH  MathSciNet  Google Scholar 

  2. L. Blum, M. Shub and S. Smale, On a theory of computation over the real numbers and complexity: NP-completeness, recursive functions, and universal machines, Bull. Amer. Math. Soc. 21 (1989) 1–46.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. T. Chong, Reducibility of Julia sets in complex analytic dynamics, preprint.

  4. A. Douady, Systèmes dynamiques holomorphes, in:Seminaire Bourkaki 105–106, Asterisque (1983) 39–63.

  5. A. Douady and H. Hubbard, Itération des polynômes quadratiques complexes, C. R. Acad. Sci. Paris 294 (1982) 123–126.

    MATH  MathSciNet  Google Scholar 

  6. M. Hirsch, Ph.D. thesis, Berkeley (1990).

  7. S. Smale, On the topology of algorithms, I, J. Complexity 3 (1987) 81–89.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. Sullivan, Quasiconformal homeomorphisms and dynamics I, Ann. Math. 122 (1985) 401–418.

    Article  MathSciNet  Google Scholar 

  9. D. Sullivan, Quasiconformal homeomorphisms and dynamics, III, preprint.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Kent Ridge, 0511, Singapore

    C. T. Chong

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  1. C. T. Chong
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Communicated by S.L. Lee

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Chong, C.T. The polynomial topological complexity of Fatou-Julia sets. Adv Comput Math 3, 369–374 (1995). https://doi.org/10.1007/BF02432003

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  • DOI: https://doi.org/10.1007/BF02432003

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