Quantifying Noninvertibility in Discrete Dynamical Systems

Colin Defant, James Propp

Given a finite set $X$ and a function $f:X\to X$, we define the degree of noninvertibility of $f$ to be $\text{deg}(f)=\frac{1}{|X|}\sum _{x\in X}|f^{-1}(f(x))|$. This…