G. Benettin

Publications88
h-index29
Citations5,566
Highly Influential Citations140
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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…
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…
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…
Kolmogorov Entropy and Numerical Experiments
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 the…
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-defined…
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…
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 ofn…
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 order…
The Steep Nekhoroshev’s Theorem
Revising Nekhoroshev’s geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev’s theorem for steep Hamiltonian systems proving, in particular, that the…
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