  This paper focuses on symmetric potentials subjected to periodic driving.
Four unperturbed potentials V_0(r) were considered, namely the Plummer
potential and Dehnen potentials with \gamma=0.0, 0.5, and 1.0, each subjected
to a time-dependence of the form V(r,t)=V_0(r)(1+m_0\sin(\omega t)). In each
case, the orbits divide clearly into regular and chaotic, distinctions which
appear absolute. In particular, transitions from regularity to chaos are
seemingly impossible. Over finite time intervals, chaotic orbits subdivide into
what can be termed `sticky' chaotic orbits, which exhibit no large scale
secular changes in energy and remain trapped in the phase space region where
they started; and `wildly chaotic' orbits, which do exhibit systematic drifts
in energy as the orbits diffuse to inhabit different phase space regions. This
latter distinction is not absolute, apparently corresponding instead to orbits
penetrating a `leaky' phase space barrier. The three different orbit types can
be identified simply in terms of the frequencies for which their Fourier
spectra have the most power. An examination of the statistical properties of
orbit ensembles as a function of driving frequency \omega allows one to
identify the specific resonances that determine orbital structure. Attention
focuses also on how, for fixed amplitude m_0, such quantities as the mean
energy shift, the relative measure of chaotic orbits, and the mean value of the
largest Lyapunov exponent vary with driving frequency \omega and how, for fixed
\omega, the same quantities depend on m_0.
