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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

On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms

- G. Benettin, A. Giorgilli
- Mathematics
- 1 March 1994

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

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
- Mathematics
- 1 December 1976

Stability of motions near resonances in quasi-integrable Hamiltonian systems

- G. Benettin, G. Gallavotti
- Mathematics, Physics
- 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
- Mathematics, 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

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

Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II

- G. Benettin, L. Galgani, A. Giorgilli
- Mathematics
- 1 March 1987

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

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

The Steep Nekhoroshev’s Theorem

- M. Guzzo, L. Chierchia, G. Benettin
- Mathematics
- 26 March 2014

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… Expand

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