The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator relate...

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Detalles Bibliográficos
Autores: Giordano, Claudia Marcela, Cincotta, Pablo Miguel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:Argentina
Institución:Universidad Nacional de La Plata
Repositorio:SEDICI (UNLP)
Idioma:inglés
OAI Identifier:oai:sedici.unlp.edu.ar:10915/141472
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/141472
Access Level:acceso abierto
Palabra clave:Astronomía
Física
Chaotic diffusion
Multidimensional dynamical systems
Entropy
Rate of diffusion
Descripción
Sumario:In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S′, estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S′ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.