04-163 A. J. Windsor

Smoothness is not an Obstruction to Exact Realizability (113K, pdf) May 25, 04

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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.

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