For a map $F: \Lambda \rightarrow \Lambda$ give the definitions of chaos according to (i) Devaney (Dchaos) and (ii) Glendinning (G-chaos).

Consider the dynamical system

$$F(x)=a x \quad(\bmod 1)$$

on $\Lambda=[0,1)$, for $a>1$ (note that $a$ is not necessarily an integer). For both definitions of chaos, show that this system is chaotic.