1999/07/31 by Yash Puri, Thomas Ward
Mathematics · #math.DS #math.NT #msc:54H20 #msc:58F20
published as Journal of Integer Sequences, 4:Article 01.2.1, 2001 · Revised version with new content; to appear in J.Integer Sequences
arxiv created 2001/04/26 · arxiv updated 2009/11/30
We give necessary and sufficient conditions for a sequence to be exactly realizable as the sequence of numbers of periodic points in a dynamical system. Using these conditions, we show that no non-constant polynomial is realizable, and give some conditions on realizable binary recurrence sequences. Realization in rate is always possible for sufficiently rapidly-growing sequences, and is never possible for slowly-growing sequences. Finally, we discuss the relationship between the growth rate of periodic points and the growth rate of points with specified least period.