Resumen de Periodic Points for Sphere Maps Preserving Monopole Foliations

Grzegorz Graff , Michal Misiurewicz, Piotr Nowak-Przygodzki

• 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.