Stabilite et probabilité dans les systèmes d'équations différentielles non linéaires: cas de cycle limite ou de solution périodique dépendant du temps: équation de Fokker-Planck du premier ordre

M. Robert Faure

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1973)

  • Volume: 54, Issue: 6, page 930-934
  • ISSN: 0392-7881

Abstract

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In the next study, the Author examines the problem of probability associated with a mehanical system Σ ⁢ ( x , y ) whose definition is two differential equations of the first order, independent of time. We study the influence of the stability of the essential elements of the trajectories of Σ : (limit-cycles, singular points) on the nature of Fokker-Planck’s solutions of equation, associated with Σ ⁢ ( x , y ) . It is proved that the density of probabilities is neither definite nor integrable to the singular stable points, and on the limit-cycles; then ρ must have the structure of distributions. When Σ is definite by differential equations with polynomes, the only case with density integrable is when there is just one single point which is a center.

How to cite

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Faure, M. Robert. "Stabilite et probabilité dans les systèmes d'équations différentielles non linéaires: cas de cycle limite ou de solution périodique dépendant du temps: équation de Fokker-Planck du premier ordre." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 54.6 (1973): 930-934. <http://eudml.org/doc/293877>.

@article{Faure1973,
author = {Faure, M. Robert},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {fre},
number = {6},
pages = {930-934},
publisher = {Accademia Nazionale dei Lincei},
title = {Stabilite et probabilité dans les systèmes d'équations différentielles non linéaires: cas de cycle limite ou de solution périodique dépendant du temps: équation de Fokker-Planck du premier ordre},
url = {http://eudml.org/doc/293877},
volume = {54},
year = {1973},
}

TY - JOUR
AU - Faure, M. Robert
TI - Stabilite et probabilité dans les systèmes d'équations différentielles non linéaires: cas de cycle limite ou de solution périodique dépendant du temps: équation de Fokker-Planck du premier ordre
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
PY - 1973
PB - Accademia Nazionale dei Lincei
VL - 54
IS - 6
SP - 930
EP - 934
LA - fre
UR - http://eudml.org/doc/293877
ER -

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