THE ROTATION NUMBER AND DIRECTION OF A CONTINUOUS FLOW ON THE TORUS
Citation：
Han Maoan.THE ROTATION NUMBER AND DIRECTION OF A CONTINUOUS FLOW ON THE TORUS[J].Chinese Annals of Mathematics B,1988,9(2):207~215
Page view： 1019Net amount： 1075
Authors：
Han Maoan;
Abstract：
In this paper the rotation direction rf and rotation number pf for any contiimons flow on the torus are defined by applying Weills theorem proved by Markley. The following
results are obtained:
(i) $\[{r_f} = 0\]$ iff all orbits of $f$ are proper and each limit set of $f$ is homotopic to zero on $\[{T^2}\]$.
(ii) if $\[{r_f} \ne 0\]$, then $\[{\rho _f}\]$ is irrational iff $f$ has at least one non-trivial $P$ stable orbit, $\[{\rho _f}\]$ is rational iff $f$ has at least one non-zero-homotopic closed or singular closed orbit.
Then a method of computing the rotation number of certain flows is given.
