Consider compact 1 dimension dynamic system. We focus on $latex S_1$, it does not mean $latex S_1$ is the only compact 1 dimensional system , but it is a typical example. $latex T: S_1\to S_1$. If $latex T$ is a homomorphism then $latex T$ stay the order of $latex S_1$ (by continuous and the zero point theorem). That is just mean: (may be do a reflexion $latex e^{2\pi i\theta}\to e^{-2\pi i\theta}$). In the homomorphism case. We try to define the rotation number to describe the expending …
