Limit point of a trajectory

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of a dynamical system

A point


(an -limit point) or


(an -limit point), where is a sequence such that as in (1), or as in (2), and for which the limits in (1) or (2) exist.

For a trajectory of a dynamical system (or, in other words, for , cf. [1]), an -limit point (-limit point) is the same as an -limit point (-limit point) of the trajectory of the dynamical system (the system with reverse time). The set () of all -limit points (-limit points) of a trajectory is called the -limit set (-limit set) of this trajectory (cf. Limit set of a trajectory).


[1] V.V. Nemytskii, V.V. Stepanov, "Qualitative theory of differential equations" , Princeton Univ. Press (1960) (Translated from Russian)


For a dynamical system with discrete time (or, a cascade) similar definitions and the same terminology are used (now in the above the sequences have to be in ).

How to Cite This Entry:
Limit point of a trajectory. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.M. Millionshchikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article