Shub's conjecture for smooth longitudinal maps of
Grzegorz Graff, Michal Misiurewicz and Piotr Nowak-Przygodzki
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.