Period Lengths for Iterated Functions

2007/11/02 by Eric Schmutz, Schmutz, Eric
Mathematics · #05A99 #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #math.CO #math.PR #msc:05A99

paper · pdf · doi:10.48550/arxiv.0711.0312

arxiv created 2007/11/02 · openalex publication_date 2007/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For random maps, the expected value of the order (i.e. the period of the sequence of compositional iterates) is approximated asymptotically. It is much smaller than the expected value for the product of the cycle lengths.

Related

• Periods of iterations of functions with restricted preimage sizes
• Law of the iterated logarithm for the periodogram
• Cycles in random k-ary maps and the poor performance of random random number generation
• Iteration entropy
• Inventory Loops (i.e. Counting Sequences) have Pre-period 2max S₁+60