The correct analysis of a given dynamical system rests on the reliable identification of the chaotic or regular behaviour of its orbits. The most commonly used tools for such analyses are based either on the study of the fundamental frequencies of the trajectories, or on the study of the evolution of the deviation vectors, the so-called variational chaos indicators (CIs hereinafter). Therefore, it seems very useful to have a tool with which one can compute several CIs in an easy and fast way. This is the main motivation of the LP-VIcode.
Present library of CIs
The library of CIs in the present version of the code includes the following: a) the Lyapunov Indicators, also known as Lyapunov Characteristic Exponents, Lyapunov Characteristic Numbers or Finite Time Lyapunov Characteristic Numbers (LIs; Benettin et al. 1976, Benettin et al. 1980); b) the Mean Exponential Growth factor of Nearby Orbits (MEGNO; Cincotta & Simó 2000, Cincotta et al. 2003); c) the Slope Estimation of the largest Lyapunov Characteristic Exponent (SElLCE; Cincotta et al. 2003); d) the Smaller ALignment Index (SALI; Skokos 2001); e) the Generalized ALignment Index (GALI; Skokos et al. 2007, Skokos et al. 2008); f) the Fast Lyapunov Indicator (FLI; Froeschlé et al. 1997, Lega & Froeschlé 2001); g) the Orthogonal Fast Lyapunov Indicator (OFLI; Fouchard et al. 2002); h) the Spectral Distance (SD; Voglis et al. 1999); i) the dynamical Spectra of Stretching Numbers (SSNs; Voglis & Contopoulos 1994, Contopoulos & Voglis 1996); and j) the Relative Lyapunov Indicator (RLI; Sándor et al. 2000, Sándor et al. 2004). The main achievement of the code is its speed: neither the orbit nor any of the sets of variational equations are computed more than once in each time step, even when they may be requested by more than one CI.