Periodic Points for Sphere Maps Preserving Monopole Foliations

• Graff, Grzegorz ^[1] ; Misiurewicz, Michał ^[2] ; Nowak-Przygodzki, Piotr
  1. [1] Gdańsk University of Technology

     Gdańsk University of Technology

     Gdańsk, Polonia

     
  2. [2] Indiana University–Purdue University
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 2, 2019, págs. 533-546
• Idioma: inglés
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  • Let S2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S2→S2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in these classes of maps.