  Many exoplanetary systems containing hot Jupiters are found to possess
significant misalignment between the spin axis of the host star and the
planet's orbital angular momentum axis. A possible channel for producing such
misaligned hot Jupiters involves Lidov-Kozai oscillations of the planet's
orbital eccentricity and inclination driven by a distant binary companion. In a
recent work (Storch, Anderson & Lai 2014), we have shown that a proto-hot
Jupiter undergoing Lidov-Kozai oscillations can induce complex, and often
chaotic, evolution of the spin axis of its host star. Here we explore the
origin of the chaotic spin behavior and its various features in an idealized
non-dissipative system where the secular oscillations of the planet's orbit are
strictly periodic. Using Hamiltonian perturbation theory, we identify a set of
secular spin-orbit resonances in the system, and show that overlaps of these
resonances are responsible for the onset of wide-spread chaos in the evolution
of stellar spin axis. The degree of chaos in the system depends on the
adiabaticity parameter $\epsilon$, proportional to the ratio of the Lidov-Kozai
nodal precession rate and the stellar spin precession rate, and thus depends on
the planet mass, semi-major axis and the stellar rotation rate. For systems
with zero initial spin-orbit misalignment, our theory explains the occurrence
(as a function of $\epsilon$) of "periodic islands" in the middle of a "chaotic
ocean" of spin evolution, and the occurrence of restricted chaos in middle of
regular/periodic spin evolution. Finally, we discuss a novel "adiabatic
resonance advection" phenomenon, in which the spin-orbit misalignment, trapped
in a resonance, gradually evolves as the adiabaticity parameter slowly changes.
This phenomenon can occur for certain parameter regimes when tidal decay of the
planetary orbit is included.
