Publications Repository - Gdańsk University of Technology

Let S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 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.

Authors

• prof. dr hab. Grzegorz Graff link open in new tab ,
• Michał Misiurewicz link open in new tab ,
• Piotr Nowak-Przygodzki