- G. Benettin, G. Orsatti and A. Ponno, On the role of the integrable Toda model in one-dimensional molecular dynamics, J. Stat. Phys. 190, 131-1:13 (2023).
- G. Benettin, S. Pasquali and A. Ponno, The Fermi-Pasta-Ulam Problem and its underlying integrable dynamics: an approach through Lyapunov Exponents, J. Stat. Phys. 171, 521-542 (2018).
- M. Guzzo, L. Chierchia and G. Benettin, The steep Nekhoroshev's theorem. Comm. Math. Phys. 342, 569-601 (2016).
-
G. Benettin, R. Livi and G. Parisi, Ergodicity: how can it be broken? in: Large deviations in physics,
Lecture Notes in Phys. 885, 29-70 (Springer, Heidelberg, 2014).
-
M. Guzzo, L. Chierchia and G. Benettin, The steep Nekhoroshev's Theorem and optimal stability exponents (an announcement).
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 25, 293-299 (2014).
-
G. Benettin, A. Ponno and H. Christodoulidi, The Fermi--Pasta--Ulam problem and its underlying integrable
dynamics, Journ. Stat. Phys. 152, 195--212 (2013).
-
G. Benettin, F. Fassò and M. Guzzo, Il corpo rigido in rapida rotazione: una moderna visione
hamiltoniana, in: Complementi alle lezioni di Meccanica
Razionale di T. Levi--Civita e U. Amaldi, E.N.M. Cirillo,
G. Maschio, T. Ruggeri and G. Saccomandi editors (Edizioni
Compumat, 2012).
-
G. Benettin and A. Ponno, Time-Scales to Equipartition in the Fermi-Pasta-Ulam
Problem: Finite-Size Effects and Thermodynamic Limit,
J. Stat. Phys. 144, 739-812 (2011).
-
G. Benettin and A. Ponno, On the numerical integration of the FPU-like systems,
Physica D 240, 568-573 (2011).
-
G. Benettin, R. Livi and A. Ponno, The Fermi-Pasta-Ulam problem:
scaling laws vs. initial conditions, Journ. Stat. Phys. 135, 873-893 (2009).
-
G. Benettin, M. Guzzo and V. Marini, Adiabatic chaos in the spin--orbit problem,
Celest. Mech. Cyn. Astr. 101, 203--224 (2008).
-
G. Benettin and G. Gradenigo, A study of the Fermi-Pasta-Ulam problem in dimension two,
CHAOS 18, 013112-1:13 (2008).
-
G. Benettin, M. Guzzo and A.I. Neishtadt,
A new problem of adiabatic invariance related to the rigid
body dynamics, Discr. Cont. Dyn. Sys. 21,
959-975 (2008).
-
G. Benettin, A. Carati, L. Galgani, A.~Giorgilli,
The Fermi-Pasta-Ulam problem and the metastability
perspective, in: G. Gallavotti ed., The Fermi-Pasta-Ulam Problem.
A status report. (Springer, Berlino 2008).
-
G. Benettin, F. Fassò e M. Guzzo,
Long term stability of proper rotations and local chaotic
motions in the perturbed Euler rigid body,
Regular and Chaotic Dynamics 11, 1-17 (2006).
-
G. Benettin, Time-scale for energy equipartition in a two-dimensional FPU model,
CHAOS 15, 015108.1-8 (2005).
-
G. Benettin, M. Guzzo e F. Fassò,
Long term stability of proper
rotations of the perturbed Euler rigid body, Commun. Math. Phys. 250, 133-160 (2004).
-
G. Benettin, The elements of Hamiltonian perturbation
theory
, lectures at the Porquerolles school 2001 "Hamiltonian
systems and Fourier analysis", D. Benest, C. Froeschle' e E. Lega editori,
Cambridge Scientific (UK), 2004.
-
G. Benettin, Physical applications of Nekhoroshev theorem and exponential estimates,
Lectures given at the Cetraro school 2000 "Hamiltonian Dynamics. Theory and Applications",
Antonio Giorgilli editore, pp. 1-73, Springer 2005.
-
G. Benettin, A.M. Cherubini and F. Fassò,
Regular and chaotic motions of the fast rotating rigid body: a numerical study.
Discrete and Continuous Dynamical Systems-Series B, Vol. 2, 521-540 (2002).
-
G. Benettin and L. Rondoni,
A new model for the transport of particles in a thermostatted system.
Mathematical Physics Electronic Journal, Volume 7 No 3, 22pp (2001).
-
G. Benettin, A.M. Cherubini and F. Fassò,
A `changing chart' symplectic algorithm for rigid bodies and other
Hamiltonian systems on manifolds.
Siam Journ, Sc. Comp. 23, 1189-1203 (2001).
-
M. Guzzo and G. Benettin,
A spectral formulation of the Nekhoroshev theorem and its relevance
for numerical and experimental data anlysis.
Discrete and Continous Dynamical Systems-Series B 1, 1-28, 2001.
-
S. Lepri, L. Rondoni and G. Benettin, The Gallavotti-Cohen
Fluctuation Theorem for a non-chaotic model.
Journ. Stat. Phys. 99, 857-872 (2000).
Elenco completo delle
pubblicazioni
Materiale didattico
PhD course "A smooth
introduction to Ergodic Theory", Autumn 2019
Notes of the course, 27/11/2019
file PDF (11 MB)
Meccanica Analitica, Corso di laurea in Fisica e in Matematica, a.a. 2016-17
Dispense
file PDF, (2.6MB)
Programma d'esame 2017-2018
file PDF
Nota sulla serie di Fourier
file PDF
Alcune prove d'esame
file PDF
Alcuni esercizi d'esame risolti
file PDF
Moti ordinati e moti caotici (breve articolo divulgativo)
file PDF
Fisica Matematica, settore di Ingegneria dell'Informazione,
a.a. 2012-2013
dispense 2/03/2017 (3.5 MB)
figure a colori 13/03/06 (1.5 MB)
eserciziario 2/03/2017 (0.9 MB)
Moti ordinati e moti caotici breve articolo divulgativo (0.4MB)
Programma 2017 - 2018 file PDF
Scuola Galileiana, "Una passeggiata tra i Sistemi Dinamici"
appunti del corso,
file PDF (16 MB)
figure a colori, 09/05/08
file PDF (2.2 MB)
Fisica Matematica per Fisica, V.O.
Dispense di "Introduzione ai sistemi dinamici":
Copertina e indice
file pdf (0.1 MB)
Capitolo I, "Introduzione alla teoria Ergodica"
file pdf (1.7 MB)
Capitolo II, "Introduzione ai sistemi dinamici iperbolici"
file PDF (1.2 MB)
Capitolo III, "Introduzione alla teoria delle perturbazioni per i
sistemi
Hamiltoniani" file pdf (1.5 MB)
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