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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $ {C^1}$ 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: http://dx.doi.org/10.1090/S0002-9939-1991-1056682-1
PII: S 0002-9939(1991)1056682-1
Article copyright: © Copyright 1991 American Mathematical Society