name of function $x_{n+1} = f(x_n)$ and the sequence it generates this is a very trivial question, but I couldn't find what the proper name a function of the form $x_{n+1} = f(x_n)$, where $f: X \rightarrow Y$ for some initial $x_0$ is, and what the the sequence $(x_n)_{n=0}^{\infty}$ which generates is called? As well what a sequence of functions $(f^{(i)})_{i=0}^{\infty}$ for $f:X \rightarrow Y$, and $f^{(m)}$ is the composure of $f$ with itself $m$ times. Thanks a bunch for your help

This is called a fixed-point iteration.