Graph components and dynamics over finite fields

Abstract

For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical systems.

12 pages

Cited by in corpus (6)

• Periods of Iterated Rational Functions over a Finite Field
• Dynamically distinguishing polynomials
• Periodic points of polynomials over finite fields
• A probabilistic heuristic for counting components of functional graphs of polynomials over finite fields
• The cycle structure of unicritical polynomials
• Permutation polynomials: iteration of shift and inversion maps over finite fields