  The reader can find in the literature a lot of different techniques to study
the dynamics of a given system and also, many suitable numerical integrators to
compute them. Notwithstanding the recent work of Maffione et al. (2011a) for
mappings, a detailed comparison among the widespread indicators of chaos in a
general system is still lacking. Such a comparison could lead to select the
most efficient algorithms given a certain dynamical problem. Furthermore, in
order to choose the appropriate numerical integrators to compute them, more
comparative studies among numerical integrators are also needed.
  This work deals with both problems. We first extend the work of Maffione et
al. (2011) for mappings to the 2D H\'enon & Heiles (1964) potential, and
compare several variational indicators of chaos: the Lyapunov Indicator (LI);
the Mean Exponential Growth Factor of Nearby Orbits (MEGNO); the Smaller
Alignment Index (SALI) and its generalized version, the Generalized Alignment
Index (GALI); the Fast Lyapunov Indicator (FLI) and its variant, the Orthogonal
Fast Lyapunov Indicator (OFLI); the Spectral Distance (D) and the Dynamical
Spectras of Stretching Numbers (SSNs). We also include in the record the
  Relative Lyapunov Indicator (RLI), which is not a variational indicator as
the others. Then, we test a numerical technique to integrate
  Ordinary Differential Equations (ODEs) based on the Taylor method implemented
by Jorba & Zou (2005) (called taylor), and we compare its performance with
other two well-known efficient integrators: the Prince & Dormand (1981)
implementation of a Runge-Kutta of order 7-8 (DOPRI8) and a Bulirsch-St\"oer
implementation. These tests are run under two very different systems from the
complexity of their equations point of view: a triaxial galactic potential
model and a perturbed 3D quartic oscillator.
