# Limit point of a trajectory

* of a dynamical system *

A point

(1) |

(an -limit point) or

(2) |

(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).

#### References

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

#### Comments

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: http://encyclopediaofmath.org/index.php?title=Limit_point_of_a_trajectory&oldid=17356