On monotone trajectories

Author:
Janusz Mierczyński

Journal:
Proc. Amer. Math. Soc. **113** (1991), 537-544

MSC:
Primary 54H20

MathSciNet review:
1056682

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Abstract: In this paper 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. Poláčik [13].

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1056682-1

Article copyright:
© Copyright 1991
American Mathematical Society