The proportion of $k$-cycles for polynomials modulo primes

Jonathan Root

Let $f(x)\in {\mathbb{F}}_p[x]$, and define the orbit of $x\in {\mathbb{F}}_p$ under the iteration of $f$ to be the set \[ \mathcal{O}(x):=\{x,f(x),(f\circ f)(x),(f\circ f\circ f)(x),…