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
).
Limit point of a trajectory. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Limit_point_of_a_trajectory&oldid=17356