  Using a purely Newtonian model for the Solar System, we investigate the
dynamics of comet 1P/Halley considering in particular the Lyapunov and power
spectra of its orbit, using the nominal initial conditions of JPL's Horizons
system. We carry out precise numerical integrations of the $(N+1)$-restricted
problem and the first variational equations, considering a time span of
$2\times10^5$~yr. The power spectra are dominated by a broadband component,
with peaks located at the current planetary frequencies, including
contributions from Jupiter, Venus, the Earth and Saturn, as well as the $1:6$
resonance among Halley and Jupiter and higher harmonics. From the average value
of the maximum Lyapunov exponent we estimate the Lyapunov time of the comet's
nominal orbit, obtaining $\tau_L \simeq 562$~yr; the remaining independent
Lyapunov exponents (not related by time-reversal symmetry) tend asymptotically
to zero as $t^{-1/2}$. Yet, our results do not display convergence of the
maximum Lyapunov exponent. We argue that the lack of convergence of the maximum
Lyapunov exponent is a signature of transient chaos which will lead to an
eventual ejection of the comet from the Solar System.
