The principle of stationary action for the Action (physics) S (a measure of the energy of the system under study)
states that the variation in S is at an extremum, in symbols:
where the independent variables are denoted by a set of xi(t) acting at some time t.
See: Action (physics) #Euler-Lagrange equations for the action integral for the conditions when this principle is true.
Extremum can in fact mean a local minimum, a local maximum, or a stationary value.