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Chaos detection tools: The LP-VIcode and its applications

Luciano Darriba, Pablo Cincotta, Nicolás Maffione, Claudia Giordano
A very important topic in galactic dynamics is the detection of instabilities of a given system and the possible appearance of chaos. Such a chaotic bahaviour can be detected and studied by means of variational chaos indicators (CIs). The CIs are based on the study of the evolution of initial deviation vectors, which makes these techniques specially sensitive to indicate the presence of chaos.

On the other hand, the so-called spectral analysis methods are based on the study of some quantity (e.g. the frequency) on a single orbit, which turns these techniques very efficient for the determination of the resonant structure of the system.

The analysis of the interaction among chaotic and regular components as well as the determination of the resonant structure of the Hamiltonian leads to a deeper understanding of the system's dynamics. Despite the advantages of the simultaneous application of both types of techniques, many researchers keep applying only one of them.

Herein, we present an alpha version of a program coded in Fortran, the LP-VIcode. Although the code is in a developing stage, it can compute several CIs, and here we apply it together with the Frequency Modified Fourier Transform (FMFT) (Sidlichovský & Nesvorný 1996) to study the stationary space (Schwarzchild 1993) of an average realistic Hamiltonian model (Muzzio et al. 2005).

Using the LP-VIcode, in Maffione et al. (2011b) and Darriba et al. (2012) the authors suggest an efficient package of CIs to study a general Hamiltonian. Here the research is extended to show that the complementary use of the LP-VIcode and the spectral analysis methods is highly recommended to study a realistic Hamiltonian model.
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