LP-VIcode features

The La Plata Variational Indicators Code (LP-VIcode for short) is an OPEN-SOURCE program specifically designed to compute a suite of variational chaos indicators

Current state

The current stable version of the code is 2.0.1, codename "Control".

NEMO friendly

The current version of the code is NEMO friendly. A front-end is under developing stage. Click here for further details.


The present library of the LP-VIcode includes 10 of the most worlwide used chaos indicators.

Output quantities

Besides the phase-space coordinates of the orbit and the chaos indicators values, the LP-VIcode provides information on the orbit's physical and geometrical properties.

Automatic differentiation

SMART module, the automatic differentiation preprocessing slave program of the LP-VIcode is almost here. Stay tune!


A parallel version in Fortran90 is on a developing stage.

User-friendly: help us!

We welcome developers that want to help us with making the code more user-friendly, for instance changing the command-driven interface to a menu-driven interface.

Library+: help us again!

Researchers that want to add their own variational chaos indicators to the present library of the code are also welcome to do it.
See below for a full introduction of the LP-VIcode

LP-VIcode motivation

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. Therefore, it seems very useful to have a tool with which one can compute several variational chaos indicators in an easy and fast way. This is the main motivation of the LP-VIcode.

Current LP-VIcode library of chaos indicators

The library of variational chaos indicators in the present version of the code includes the following:


The Lyapunov Indicators, a.k.a. Lyapunov Characteristic Exponents, Lyapunov Characteristic Numbers or Finite Time Lyapunov Characteristic Numbers (LIs; Benettin et al. 1976, Benettin et al. 1980).


The Mean Exponential Growth factor of Nearby Orbits (MEGNO; Cincotta and Simó2000, Cincotta et al. 2003). The Slope Estimation of the largest Lyapunov Characteristic Exponent (SElLCE; Cincotta et al. 2003).


The Smaller ALignment Index (SALI; Skokos 2001). The Generalized ALignment Index (GALI; Skokos et al. 2007, Skokos et al. 2008).


The Fast Lyapunov Indicator (FLI; Froeschlé et al. 1997, Lega and Froeschlé 2001). The Orthogonal Fast Lyapunov Indicator (OFLI; Fouchard et al. 2002).


The Spectral Distance (SD; Voglis et al. 1999).


The dynamical Spectra of Stretching Numbers (SSNs; Voglis and Contopoulos 1994, Contopoulos and Voglis 1996).


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 variational chaos indicator.


The literature behind the development of the LP-VIcode
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The PhD thesis that presents a thoroughly comparative study of the most used chaos indicators in the literature, which includes a series of papers where the earliest versions of the LP-VIcode were applied.

Link to Download
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The Alpha version

The paper that introduces the first version of the LP-VIcode.

Link to download
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The first stable version of the LP-VIcode

The paper that fully describes the completely rewritten and first stable version of the LP-VIcode, version 1.0.2. codename "KAOS".

Link to download


Here you can download the User Guide, the current version of the code as well as examples of potentials to test your own

User Guide

  • Latest version, 2.0.1
  • Step by step configuration, compilation and execution
  • Full and easy examples to follow


The Code

  • Latest version: LP-VIcode "Control"
  • Input files
  • Parameter files


  • The 2D Henon-Heiles potential
  • The 2D Logarithmic potential
  • A 3D triaxial extension of the Navarro-Frenk-White dark matter halo potential

Before you download and go, please take a look at the ongoing and future developments below!


ONGOING IMPLEMENTATIONS: The SMART module is an automatic differentiation preprocessing slave program of the LP-VIcode that computes the accelerations and variational equations with the only input of the potential function. There is no need to calculate the accelerations and variational equations any more. The implementation is on a validation stage and we hope it can be realeased soon. Stay tune to get SMART!

FUTURE DEVELOPMENTS: A parallel version entirely written in Fortran90 is on an early developing stage.

SMART: Automatic differentiation module


The main goal of the LP-VIcode project is to cluster in a single, easy-to-use tool the plethora of variational chaos indicators that are nowadays in the literature. We intend to motivate researchers to collaborate with their own methods in developing newer versions of the code with larger variational chaos indicators' libraries. You can also make suggestions to improve the code or report a bug.

Or just in case you want to get in touch with us, please fill the form below and we will contact you as soon as possible. Thank you!

And Last but not Least: Meet Our Team

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The Chief
Dynamics of stellar and planetary systems
Daniel Carpintero
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Formation and evolution of planetary systems
Luciano Darriba
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The impact of chaos in Milky Way-type galaxies
Nicolás Maffione