Suppose we have a smooth dynamical system on $R^n$ (defined by a system of ODEs). Assume that:

(1) The system has an absorbing ball, that is every trajectory eventually enters this ball and stays in it.

(2) The system has a unique stationary point, and this stationary point is locally asymptotically stable.

(2) The system has no period orbits.

Can we conclude that the stationary point is in fact *globally* stable?