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Probabilistic approach to homoclinic chaos

par Daems, David ;Nicolis, Grégoire
Référence Journal of Statistical Physics, 76, 5-6, page (1287-1305)
Publication Publié, 1994

Article révisé par les pairs

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Résumé :

Three-dimensional systems possessing a homoclinic orbit associated to a saddle focus with eigenvalues ρ{variant}±iω, -λ and giving rise to homoclinic chaos when the Shil'nikov condition ρ{variant}<λ is satisfied are studied. The 2D Poincaré map and its 1D contractions capturing the essential features of the flow are given. At homoclinicity, these 1D maps are found to be piecewise linear. This property allows one to reduce the Frobenius-Perron equation to a master equation whose solution is analytically known. The probabilistic properties such as the time autocorrelation function of the state variable x are explicitly derived. © 1994 Plenum Publishing Corporation.