1990/05/01 by John Franks, Michał Misiurewicz, Michal Misiurewicz
Mathematics · #Mathematical Dynamics and Fractals #Geometric Analysis and Curvature Flows #Mathematics and Applications
paper · pdf · doi:10.2307/2048385
We consider the rotation set >(<t>) for a lift 4> = "P,^ of a flow ip = <pt : T -> T",K Our main result is that p(<t>) consists of either a single point, a segment of a line through 0 with rational slope, or a line segment with irrational slope and one endpoint equal to 0 .Any set of one of these types is the rotation set for some flow.In this article we consider the rotation set as defined in [MZ], for a lift * = W,R of a flow 9 = (ft : t2 -j2<eR (1.1) Definition.The rotation set p(<J>) of a flow <I> on the plane is defined by v e p(<i>) if and only if there are sequences x e R~ and t 6 E+ with lim /. = oo such that