  Animal behavior is often quantified through subjective, incomplete variables
that may mask essential dynamics. Here, we develop a behavioral state space in
which the full instantaneous state is smoothly unfolded as a combination of
short-time posture dynamics. Our technique is tailored to multivariate
observations and extends previous reconstructions through the use of maximal
prediction. Applied to high-resolution video recordings of the roundworm
\textit{C. elegans}, we discover a low-dimensional state space dominated by
three sets of cyclic trajectories corresponding to the worm's basic stereotyped
motifs: forward, backward, and turning locomotion. In contrast to this broad
stereotypy, we find variability in the presence of locally-unstable dynamics,
and this unpredictability shows signatures of deterministic chaos: a collection
of unstable periodic orbits together with a positive maximal Lyapunov exponent.
The full Lyapunov spectrum is symmetric with positive, chaotic exponents
driving variability balanced by negative, dissipative exponents driving
stereotypy. The symmetry is indicative of damped, driven Hamiltonian dynamics
underlying the worm's movement control.
