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Fatou- and Julia-Like Sets

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Ukrainian Mathematical Journal Aims and scope

For a family of holomorphic functions on an arbitrary domain, we introduce Fatou- and Julia-like sets and establish some interesting properties of these sets.

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References

  1. A. F. Beardon, “Iteration of rational functions,” Grad. Texts in Math., 132, Springer-Verlag, New York (1991).

  2. W. Bergweiler, “Iteration of meromorphic functions,” Bull. Amer. Math. Soc. (N.S.), 29, 151–188 (1993).

    Article  MathSciNet  Google Scholar 

  3. C. Caratheodory, Theory of Functions of a Complex Variable, Vol. 2, Chelsea Publishing Co., New York (1954).

  4. L. Carleson and T. W. Gamelin, Complex Dynamics, Springer, New York (1993).

    Book  Google Scholar 

  5. M. Cristea, “Open discrete mappings having local ACLn inverses,” Complex Var. Elliptic Equ., 55, No. 1-3, 61–90 (2010).

    Article  MathSciNet  Google Scholar 

  6. W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford (1964).

    MATH  Google Scholar 

  7. A. Hinkkanen and G. J. Martin, “The dynamics of semigroups of rational functions, I,” Proc. London Math. Soc. (3), 73, No. 2, 358–384 (1996).

    Article  MathSciNet  Google Scholar 

  8. D. A. Kovtonyuk, V. I. Ryazanov, R. R. Salimov, and E. A. Sevost’yanov, “Toward the theory of Orlicz–Sobolev classes,” St. Petersburg Math. J., 25, No. 6, 929–963 (2014).

    Article  MathSciNet  Google Scholar 

  9. O. Martio, S. Rickman, and J. Väisälä, “Distortion and singularities of quasiregular mappings,” Ann. Acad. Sci. Fenn. Ser. AI, 465 (1970), 13 pp.

  10. R. Miniowitz, “Normal families of quasimeromorphic mappings,” Proc. Amer. Math. Soc., 84, No. 1, 35–43 (1982).

    Article  MathSciNet  Google Scholar 

  11. V. I. Ryazanov, R. R. Salimov, and E. A. Sevost’yanov, “On convergence analysis of space homeomorphisms,” Sib. Adv. Math., 23, No. 4, 263–293 (2013).

    Article  MathSciNet  Google Scholar 

  12. J. L. Schiff, Normal Families, Springer-Verlag, New York (1993).

    Book  Google Scholar 

  13. W. Schwick, “Repelling periodic points in the Julia sets,” Bull. London Math. Soc., 29, No. 3, 314–316 (1997).

    Article  MathSciNet  Google Scholar 

  14. N. Steinmetz, Rational Iteration, Walter de Gruyter, Berlin (1993).

    Book  Google Scholar 

  15. L. Zalcman, “Normal families: New perspectives,” Bull. Amer. Math. Soc. (N.S.), 35, No. 2, 215–230 (1998).

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Jammu, Jammu, India

    K. S. Charak, A. Singh & M. Kumar

Authors
  1. K. S. Charak
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  2. A. Singh
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  3. M. Kumar
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Corresponding author

Correspondence to M. Kumar.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 10, pp. 1432–1438, October, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i10.802.

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Charak, K.S., Singh, A. & Kumar, M. Fatou- and Julia-Like Sets. Ukr Math J 73, 1654–1661 (2022). https://doi.org/10.1007/s11253-022-02021-5

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  • DOI: https://doi.org/10.1007/s11253-022-02021-5

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