Journal
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
Volume 130, Issue 11, Pages -Publisher
SPRINGER
DOI: 10.1007/s10569-018-9871-3
Keywords
Shannon entropy; Phase correlations; Diffusion
Funding
- Consejo Nacional de Investigaciones Cientificas y Tecnicas de la Republica Argentina (CONICET)
- Universidad Nacional de La Plata
- Instituto de Astrofisica de La Plata
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In the present work, we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments, we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when dealing with a chaotic diffusion process. We apply this approach to different low-dimensional maps in order to show that indeed the entropy is very sensitive to the presence of correlations among the successive values of angular variables, even when it is weak. Later on, we apply this approach to unveil strong correlations in the time evolution of the phases involved in the Arnold's Hamiltonian that lead to anomalous diffusion, particularly when the perturbation parameters are comparatively large. The obtained results allow us to discuss the validity of several approximations and assumptions usually introduced to derive a local diffusion coefficient in multidimensional near-integrable Hamiltonian systems, in particular the so-called reduced stochasticity approximation.
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