# Periodic trajectory

From Encyclopedia of Mathematics

*of an autonomous system of ordinary differential equations*

The trajectory of a periodic solution to this system; it is usually understood that this solution does not reduce to a constant, i.e. that the trajectory does not reduce to one point (an equilibrium position). A synonym of periodic trajectory is closed trajectory (because it is a closed curve).

#### Comments

For literature on the existence of periodic trajectories, see Periodic point.

**How to Cite This Entry:**

Periodic trajectory. D.V. Anosov (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Periodic_trajectory&oldid=15740

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098