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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
- G. Benettin, L. Galgani, A. Giorgilli, J. Strelcyn
- Mathematics
- 1 March 1980
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
Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application
- G. Benettin, L. Galgani, A. Giorgilli, J. Strelcyn
- Mathematics
- 1 March 1980
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
Kolmogorov Entropy and Numerical Experiments
- G. Benettin, L. Galgani, J. Strelcyn
- Physics
- 1 December 1976
Stability of motions near resonances in quasi-integrable Hamiltonian systems
- G. Benettin, G. Gallavotti
- Mathematics
- 1 August 1986
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… Expand
Numerical experiments on the free motion of a point mass moving in a plane convex region: Stochastic transition and entropy
- G. Benettin, J. Strelcyn
- Physics
- 1 February 1978
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… Expand
Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I
- G. Benettin, L. Galgani, A. Giorgilli
- Mathematics
- 1 March 1987
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
A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems
- G. Benettin, L. Galgani, A. Giorgilli
- Mathematics
- 1 September 1985
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
Nekhoroshev-Stability of Elliptic Equilibria of Hamiltonian Systems
- F. Fassò, M. Guzzo, G. Benettin
- Mathematics
- 1 October 1998
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… Expand
Kolmogorov entropy of a dynamical system with an increasing number of degrees of freedom
- G. Benettin, C. Froeschlé, J. Scheidecker
- Physics
- 1 June 1979
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 uniform… Expand
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… Expand