Functiones et Approximatio Commentarii Mathematici

Homotopy minimal periods of holomorphic maps on surfaces

Jaume Llibre and Wacław Marzantowicz

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Abstract

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 $\geq 2$.

Article information

Source
Funct. Approx. Comment. Math., Volume 40, Number 2 (2009), 309-326.

Dates
First available in Project Euclid: 1 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.facm/1246454033

Digital Object Identifier
doi:10.7169/facm/1246454033

Mathematical Reviews number (MathSciNet)
MR2543560

Zentralblatt MATH identifier
1182.55003

Subjects
Primary: 55M20: Fixed points and coincidences [See also 54H25]
Secondary: 57N05: Topology of $E^2$ , 2-manifolds 57N10: Topology of general 3-manifolds [See also 57Mxx]

Keywords
Set of periods periodic points holomorphic maps homotopy Riemann surfaces

Citation

Llibre, Jaume; Marzantowicz, Wacław. Homotopy minimal periods of holomorphic maps on surfaces. Funct. Approx. Comment. Math. 40 (2009), no. 2, 309--326. doi:10.7169/facm/1246454033. https://projecteuclid.org/euclid.facm/1246454033


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