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dc.contributor.author
Cincotta, Pablo Miguel
dc.contributor.author
Shevchenko, Ivan I.
dc.date.available
2021-10-28T15:33:39Z
dc.date.issued
2020-01-15
dc.identifier.citation
Cincotta, Pablo Miguel; Shevchenko, Ivan I.; Correlations in area preserving maps: A Shannon entropy approach; Elsevier Science; Physica D - Nonlinear Phenomena; 402; 15-1-2020; 1-26
dc.identifier.issn
0167-2789
dc.identifier.uri
http://hdl.handle.net/11336/145349
dc.description.abstract
In the present work we extend and generalize the formulation of the Shannon entropy as a measure of correlations in the phase space variables of any dynamical system. By means of theoretical arguments we show that the Shannon entropy is a quite sensitive approach to detect correlations in the state variables. The formulation given herein includes the analysis of the evolution of a single variable of the system, for instance a given phase; the phase space variables of a 2-dimensional model or the action space of a 4-dimensional map or a 3dof Hamiltonian. We show that the Shannon entropy provides a direct measure of the volume of the phase space occupied by a given trajectory as well as a direct measure of the correlations among the successive values of the phase space variables in any dynamical system, in particular when the motion is highly chaotic. We use the standard map model at large values of the perturbation parameter to confront all the analytical estimates with the numerical simulations. The numerical–experimental results show the efficiency of the entropy in revealing the fine structure of the phase space, in particular the existence of small stability domains (islands around periodic solutions) that affect the diffusion.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier Science
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
AREA PRESERVING MAPS
dc.subject
CHAOTIC DIFFUSION
dc.subject
SHANNON ENTROPY
dc.subject.classification
Astronomía
dc.subject.classification
Ciencias Físicas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Correlations in area preserving maps: A Shannon entropy approach
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2020-11-19T21:57:18Z
dc.journal.volume
402
dc.journal.pagination
1-26
dc.journal.pais
Países Bajos
dc.journal.ciudad
Amsterdam
dc.description.fil
Fil: Cincotta, Pablo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina
dc.description.fil
Fil: Shevchenko, Ivan I.. Saint Petersburg State University; Rusia
dc.journal.title
Physica D - Nonlinear Phenomena
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://doi.org/10.1016/j.physd.2019.132235
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S016727891930065X?via%3Dihub
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