Shub's conjecture for smooth longitudinal maps of Sm

Grzegorz Graff, Michal Misiurewicz and Piotr Nowak-Przygodzki


Abstract

Let  f  be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of  f, reduce the Shub's conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m=2 and in a weak form for m=3.