  We investigate precursors of critical behavior in the quasienergy spectrum
due to the dynamical instability in the kicked top. Using a semiclassical
approach, we analytically obtain a logarithmic divergence in the density of
states, which is analogous to a continuous excited state quantum phase
transition in undriven systems. We propose a protocol to observe the cusp
behavior of the magnetization close to the critical quasienergy.
