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On monotone trajectories
Proceedings of the American Mathematical Society
In this paper C strongly monotone dynamical systems are investigated. It is proved that the set of points with precompact orbits which converge to a not unstable equilibrium but whose trajectories are not eventually strongly monotone is nowhere dense. This improves on and extends a recent result by P. Polácik  . For a metric space X with metric d, by a semiflow on X we mean a continuous mapping tp: [0, oo) x X -► X satisfying the following (we denote 0. We say a point x £ X (or itsdoi:10.1090/s0002-9939-1991-1056682-1 fatcat:vptcipwwsve4vn7qc3vfgz54gm