Shannon entropy diffusion estimates: sensitivity on the parameters of the method

Celestial Mechanics and Dynamical Astronomy volume 133, Article number: 7 (2021) Cite this article

Abstract

In the present effort, we revisit the Shannon entropy approach for the study of both the extent and the rate of diffusion in a given dynamical system. In particular, we provide a theoretical and numerical study of the dependence of the formulation on the parameters of the method. We succeed in deriving not only a diffusion coefficient, \(D_{S}\), but also an estimate of the macroscopical instability time for the system under study. Dealing with a toy model, namely a 4D symplectic application that represents the dynamics around a junction of resonances of different order, and an a particular case of the planar three-body problem, the HD20003 planetary system, we obtain numerical evidence that \(D_{S}\) is a robust measure of the diffusion rate, no significant dependence on the free parameter of the entropy formulation (the size of the elements of the partition) being observed. Moreover, successful results concerning the estimation of macroscopical instability times obtained from \(D_{S}\) are presented in both cases.

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Acknowledgements

This work was supported by grants from Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina (CONICET), the Universidad Nacional de La Plata and the Universidad Nacional de Córdoba, IAG-USP and CAPES. We are very grateful to Carles Simó for his valuable comments that allow us to improve the manuscript. Two anonymous reviewers are also acknowledged for their criticism that helped us to improve this manuscript.

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Affiliations

  1. Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astonómicas y Geofísicas, Universidad Nacional de La Plata, La Plata, Argentina

    Pablo M. Cincotta & Claudia M. Giordano

  2. Instituto de Astrofísica de La Plata (CONICET-UNLP), La Plata, Argentina

    Pablo M. Cincotta & Claudia M. Giordano

  3. Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, São Paulo, Brazil

    Raphael Alves Silva

  4. Instituto de Astronomía Teórica y Experimental (IATE), Observatorio Astronómico, Universidad Nacional de Córdoba, Córdoba, Argentina

    Cristián Beaugé

Authors
  1. Pablo M. Cincotta
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  2. Claudia M. Giordano
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  3. Raphael Alves Silva
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  4. Cristián Beaugé
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Correspondence to Pablo M. Cincotta.

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Cincotta, P.M., Giordano, C.M., Silva, R.A. et al. Shannon entropy diffusion estimates: sensitivity on the parameters of the method. Celest Mech Dyn Astr 133, 7 (2021). https://doi.org/10.1007/s10569-021-10006-y

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Keywords

  • Chaotic diffusion
  • Resonances
  • Shannon entropy
  • Three-body problem