Homotopy minimal periods of holomorphic maps on surfaces

Jaume Llibre, Wacław Marzantowicz

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5 Citations (Scopus)


© Wydawnictwo Naukowe UAM, Poznań 2009. In this paper we study the minimal periods on a holomorphic map which are preserved by any of its deformation considering separately the case of continuous and holomorphic homotopy. A complete description of the set of such minimal periods for holomorphic self-map of a compact Riemann surface is given. It shows that a nature of answer depends on the geometry of the surface distinguishing the parabolic case of the Riemann sphere, elliptic case of tori and the hyperbolic case of a surface of genus ≤ 2.
Original languageEnglish
Pages (from-to)309-326
JournalFunctiones et Approximatio, Commentarii Mathematici
Issue number2
Publication statusPublished - 1 Jan 2009


  • Holomorphic maps
  • Homotopy
  • Periodic points
  • Riemann surfaces
  • Set of periods


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