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

Comparative study of variational chaos indicators and ODEs' numerical integrators