Journal of Applied Mathematics and Computing

, Volume 46, Issue 1–2, pp 201–214 | Cite as

Recurrence analysis on Julia sets of semigroups of complex polynomials

  • Gerardo R. Chacón
  • Renato Colucci
  • Daniele D’Angeli
Original Research


We introduce a recurrence function in order to analyze the dynamics of semigroups of complex polynomials. We show that under a regularity hypothesis, the recurrence function is continuous in the complex plane. This is a new notion even for the case of a semigroup with just one generator.


Time series analysis Semigroups of analytic functions Julia set Complex dynamics 

Mathematics Subject Classification (2000)

37M10 37F50 



The authors would like to thank Mr.Arnold Ramírez for developing the code of some of the software needed for the experiments. The authors would also like to thank the anonymous referees for their useful suggestions and for pointing out several important references.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2013

Authors and Affiliations

  • Gerardo R. Chacón
    • 1
  • Renato Colucci
    • 1
  • Daniele D’Angeli
    • 2
  1. 1.Pontificia Universidad JaverianaBogotáColombia
  2. 2.Institut für Mathematische Strukturtheorie (Math C)Technische Universität GrazGrazAustria

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