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Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory
SommarioDa diversi anni gli esponenti caratteristici di Lyapunov sono divenuti di notevole interesse nello studio dei sistemi dinamici al fine di caratterizzare quantitativamente le proprietà diExpand
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Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application
SommarioQuesto articolo, insieme con il precedente (Parte 1: Teoria, pubblicato in questa stessa rivista) è inteso a fornire un metodo esplicito per il calcolo di tutti gli esponenti caratteristiciExpand
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A proof of the estimation from below in Pesin's entropy formula
We give a proof of Pesin entropy formula in a very general setting.
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Numerical experiments on the free motion of a point mass moving in a plane convex region: Stochastic transition and entropy
We numerically investigate the behavior of a simple dynamical system, a plane billiard which by a continuous deformation of the border passes from a completely integrable system to a well-definedExpand
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On the non-existence of constants of derivations: the proof of a theorem of Jouanolou and its development
En nous inspirant de la demonstration d'un theoreme de non-integrabilite de J.-P. Jouanolou, nous decrivons une methode generale pour prouver l'absence de constantes non-triviales pour certainesExpand
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On the algebraic non-integrability of Halphen system
Abstract It is proved that the Halphen system of ordinary differential equations has no non-trivial rational first integrals.
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Isochronicity conditions for some planar polynomial systems
We study the isochronicity of centers at $O\in \mathbb{R}^2$ for systems $\dot x=-y+A(x,y), \dot y=x+B(x,y)$, where $A, B\in \mathbb{R}[x,y]$, which can be reduced to the Lienard type equation. UsingExpand
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On the reliability of numerical studies of stochasticity
SummaryIn the numerical study of classical dynamical systems presenting stochastic behaviour one frequently makes use, in an explicit or an implicit way, of the Birkhoff ergodic theorem. The correctExpand
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Numerical integration of differential equations in the presence of first integrals: observer method
We introduce a simple and powerful procedure—the observer method—in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinaryExpand
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