Yash Puri, Thomas Ward
Published 1999-07-01, updated 2001-04-26Version 2
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.
Comments: Revised version with new content; to appear in J.Integer Sequences
Journal: Journal of Integer Sequences, 4:Article 01.2.1, 2001
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