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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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Stability of motions near resonances in quasi-integrable Hamiltonian systems
Nekhoroshev's theorem on the stability of motions in quasi-integrable Hamiltonian systems is revisited. At variance with the proofs already available in the literature, we explicitly consider theExpand
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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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Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I
The so-called problem of the realization of the holonomic constraints of classical mechanics is here revisited, in the light of Nekhoroshev-like classical perturbation theory. Precisely, ifExpand
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A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems
In the present paper we give a proof of Nekhoroshev's theorem, which is concerned with an exponential estimate for the stability times in nearly integrable Hamiltonian systems. At variance with theExpand
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Nekhoroshev-Stability of Elliptic Equilibria of Hamiltonian Systems
Abstract: We prove a conjecture by N.N. Nekhoroshev about the long-time stability of elliptic equilibria of Hamiltonian systems, without any Diophantine condition on the frequencies. Higher orderExpand
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Kolmogorov entropy of a dynamical system with an increasing number of degrees of freedom
Lyapunov characteristic numbers are used to estimate numerically the Kolmogorov entropy of an isolated one-dimensional self-gravitating system consisting of $N$ plane parallel sheets with uniformExpand
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Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II
As in Part I of this paper, we consider the problem of the energy exchanges between two subsystems, of which one is a system of ν harmonic oscillators, while the other one is any dynamical system ofnExpand
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