Two simple and efficient numerical methods to explore the phase space struc
ture are presented, based on the properties of the "dynamical spectra". 1)
We calculate a "spectral distance" D of the dynamical spectra for two diffe
rent initial deviation vectors. D --> 0 in the case of chaotic orbits, whil
e D --> const not equal 0 in the case of ordered orbits. This method is by
orders of magnitude faster than the method of the Lyapunov Characteristic N
umber (LCN). 2) We define a sensitive indicator called ROTOR (ROtational TO
ri Recongnizer) for 2D maps. The ROTOR remains zero in time on a rotational
torus, while it tends to infinity at a rate proportional to N = number of
iterations, in any case other than a rotational torus. We use this method t
o locate the last KAM torus of an island of stability, as well as the most
important cantori causing stickiness near it.