$Let (F, X) = $ dynamical system
Part 1: Prove that if $F(a) = a$ such that a $\epsilon$ X (a is a fixed point of F), then the basin of attraction of $a$ , $A_a$ is non-empty.
Def'n: Let (F, X) = dynamical system and let a $\epsilon$ X. The basin of attraction
of a is the set $A_a$ = {y $\epsilon$ X : $\lim_{a\to \infty} F^{n}y = a$}
Should I use proof by contradiction here?
Part 2: Fix b $\epsilon$ X. Prove that if R $\subseteq$ $A_{y}$(basin of attractn)then $F(R^{-1})$ $\subseteq$ $A_{y}$.