Random functions from coupled dynamical systems

Abstract

Let $f:T⟶T$ be a mapping and $\Omega$ be a subset of $T$ which intersects every (positive) orbit of $f$. Assume that there are given a second dynamical system $\lambda :Y⟶Y$ and a mapping $\alpha :\Omega ⟶Y$. For $t\in T$ let $\delta (t)$ be the smallest $k$ such that $f^k(t)\in \Omega$ and let $t_{\Omega }:=f^{\delta (t)}(t)$ be the first element in the orbit of $t$ which belongs to $\Omega$. Then we define a mapping $F:T⟶Y$ by $F(t):={\lambda }^{\delta (t)}(t_{\Omega })$.

arXiv comment17 pages