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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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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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Formal integrals for an autonomous Hamiltonian system near an equilibrium point
In this paper we give a new method to construct formal integrals for an autonomous Hamiltonian system near an equilibrium point. Our construction is reminiscent of the algorithms introduced by HoriExpand
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Localization of energy in FPU chains
We revisit the celebrated model of Fermi, Pasta and Ulam with the aim of investigating, by numerical computations, the trend towards equipartition in the thermodynamic limit. We concentrate our Expand
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On the number of isolating integrals in Hamiltonian systems
In a Hamiltonian system of three degrees of freedom we have found a large stochastic region (the "big sea"), some other stochastic regions, apparently separated from the above ("small seas"), andExpand
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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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Rigorous estimates for the series expansions of Hamiltonian perturbation theory
In the present paper we prove a theorem giving rigorous estimates in the problem of bringing to normal form a nearly integrable Hamiltonian system, using methods of classical perturbation theory,Expand
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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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