A. Giorgilli

Publications98
h-index32
Citations4,962
Highly Influential Citations149
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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 di… Expand
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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 caratteristici… Expand
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On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms
We reconsider the problem of the Hamiltonian interpolation of symplectic mappings. Following Moser's scheme, we prove that for any mapping ψε, analytic and ε-close to the identity, there exists an… Expand
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Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
Abstract We consider an n -degrees of freedom Hamiltonian system near an elliptic equilibrium point. The system is put in normal form (up to an arbitrary order and with respect to some resonance… Expand
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Superexponential stability of KAM tori
We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size… Expand
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Notes on exponential stability of Hamiltonian systems
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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, if… Expand
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Exponentially long times to equipartition in the thermodynamic limit
Abstract We investigate with numerical methods the scaling of the relaxation time to equipartition in the celebrated Fermi–Pasta–Ulam model. Our numerical results strongly suggest that the time… Expand
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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 the… Expand
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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 Hori… Expand
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