The fully nonlinear notion of resonance -geometrical聽resonance- in
the general context of dissipative systems subjected to nonsteady
potentials is discussed. It is demonstrated that there is an exact local
invariant associated with each geometrical resonance solution which reduces to
the system's energy when the potential is steady. The geometrical resonance
solutions represent a \textit{local symmetry} whose critical breaking leads to
a new analytical criterion for the order-chaos threshold. This physical
criterion is deduced in the co-moving frame from the local energy conservation
over the shortest significant timescale. Remarkably, the new criterion for the
onset of chaos is shown to be valid over large regions of parameter space, thus
being useful beyond the perturbative regime and the scope of current
mathematical techniques