A. J. Windsor
Smoothness is not an Obstruction to Exact Realizability
(113K, pdf)

ABSTRACT.  A sequence of non-negative integers {a(n)} is called exactly realizable if there is a map T of a set X such that this sequence describes the number of periodic points, i.e. a(n) is the number of points of period n for the map T. We prove that any exactly realizable sequence can be realized by a infnitely differentiable diffeomorphism of the 2-torus. This addresses a question raised by Y. Puri.