- Università di
Padova Dipartimento di Matematica
Pura ed ApplicataFrancesco Fassò |

Publications

(The postscript files for the prepints of the new articles and of some of those already published can be downloaded by clicking on the Preprint icon. Please note that the preprint may differ from the published article: existing laws forbid (I think) to modify preprints after the transfer of copyright. Should you be interested in a reprint of the article, please contact me)

[50] **Moving energies as first integrals of
nonholonomic systems with affine constraints Preprint
(revised version)
**To be published in Nonlinearity

(with L. Garcia-Naranjo and N. Sansonetto)

[49] **Quantum manifestations of Nekhoroshev stability
**Physics Letters A

(with D. Fontanari and D. Sadovskii)

[48] **An application of Nekhoroshev theory to the study of the perturbed hydrogen atom ****
Preprint
**Mathematical Physics, Analysis and
Geometry

[47] **Conservation of energy and momenta in
nonholonomic systems with affine constraints** **
Preprint
** Regular and Chaotic Dynamics

(with N. Sansonetto)

[46] **Conservation of `moving' energy in
nonholonomic systems with affine constraints and integrability of spheres on
rotating surfaces
Preprint
**Journal of Nonlinear Science

(with N. Sansonetto)

[45] **No monodromy in the champagne bottle,
or
singularities of a superintegrable system Preprint
Journal of Geometric Mechanics **

(with L. Bates)

[44] **Quasi-periodicity in relative
quasi-periodic tori. Preprint
**Nonlinearity

(with A. Giacobbe and L. Garcia-Naranjo)

[43] **The Hamilton-Jacobi equation,
integrability, and nonholonomic systems.
Preprint
- PDF **

Journal of Geometric Mechanics **6**
(2014), 441-449

(with L. Bates and N. Sansonetto)

[42]** ****Erratum to: Stability
properties of the Riemann ellipsoids**.
Preprint
- PDF

Arch. Ration. Mech. Anal. **212**
(2014), 1065-1069.

(with D. Lewis)

[41] **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).

(with G. Benettin and M.Guzzo)

[40] **Linear weakly Noetherian constants
of motion are horizontal gauge momenta. **
Preprint
- PDF

Journal of Geometric Mechanics **4 **(2012), 129-136.

(with A. Giacobbe and N. Sansonetto)

[39] **On the number of Weakly--Noetherian constants of motions of nonholonomic
systems. **Preprint
- PDF

Journal of Geometric Mechanics **4**, 389-416 (2009)

(with A. Giacobbe and N. Sansonetto)

[38] **An elemental overview of the nonholonomic Noether theorem. **Preprint
- PDF **
**International Journal of Geometric Methods in Modern Physics

(with N. Sansonetto)

[37]

Reports on Mathematical Physics

(with A. Giacobbe and N. Sansonetto)

[36]

(with E. Celledoni, N. Safstrom and A. Zanna)

[35] ** An affine model for the actions in
an integrable system with monodromy
**Regular and Chaotic Dynamics

(with L. Bates)

[34] ** The reaction-annihilator distribution
and the nonholonomic Noether theorem for lifted actions. **** **Revised
version - PDF **
** Regular and Chaotic Dynamics

(with A. Ramos and N. Sansonetto)

[33] ** Integrable almost--symplectic
Hamiltonian systems. **** **Preprint
- PDF **
** Journal of Mathematical Physics

(with N. Sansonetto)

[32] **Geometry of invariant tori of
certain integrable systems with symmetry and an application to a nonholonomic
system. **** **Article
- PDF **
** Sigma-Symmetry, Integrability and Geometry: Methods and
Applications

(with A. Giacobbe)

[31] **Geometry of KAM
tori for nearly integrable Hamiltonian systems **Preprint -
PDF **
** Ergodic Theory and Dynamical Systems

(with H. Broer, R. Cushman and F. Takens)

[30] **The conjugate locus for the Euler top.
I. The axisymmetric case. **Preprint
- Zipped PS

International Mathematical Forum **2** (43), 2109-2139 (2007).

(with L. Bates)

[29] **Long--term stability of proper rotations
and local chaotic motions in the perturbed Euler
rigid body **

Regular and Chaotic Mechanics **11**, 267-284 (2006).

(with G. Benettin and M. Guzzo)

[28] **Superintegrable Hamiltonian systems:
geometry and perturbations.
** Acta Applicandae Mathematicae

[27] **Periodic
flows, Poisson structures, and
Nonholonomi mechanics. ** Preprint
(Second version, 2005) -PS

Regular and Chaotic Mechanics **10**, 267-284 (2005).

(with A. Giacobbe and N. Sansonetto)

[26] **A Hamiltonian KAM theorem for
bundles of Lagrangean tori
**In: F. Dumortier, H.W. Broer, J. Mahwin and S.M. Verduyn-Lunel (eds),
EQUADIFF 2003, pg 696--701 (World Scientific, Singapore, 2005)

(with H. Broer and R. Cushman)

[25] **Long--term stability of proper rotations of the perturbed
Euler rigid body **Preprint
(revised version)-PS

Communications in Mathematical Physics **250**,
133-160 (2004)

(with G. Benettin and M. Guzzo)

[24] **An algorithm for detecting Directional
Quasi-Convexity **Preprint
(revised version) - PS**
** BIT - Numerical Mathematics

(with H.Dullin)

[23] **Comparison of splitting algorithms for the
rigid body **Preprint-PS

Journal of Computational Physics (Vol. **189**, 527-538, 10 August 2003)

[22] **Geometric structure of "broadly
integrable" Hamiltonian systems **Preprint-PS

Journal of Geometry and Physics **44**, 156-170 (2002)

(with A. Giacobbe)

[21] **Regular and chaotic motions of the fast
rotating rigid body: a numerical study **Preprint-PS
(3.7 MB) Preprint-ZippedPS (1.2 MB)

Discrete and Continuos Dynamical Systems, Series B **2,**521--540 (2002)

(with G. Benettin and A.M. Cherubini)

[20] **A "changing chart" symplectic algorithm
for rigid bodies and other Hamiltonian systems on manifolds" **Preprint-PS

SIAM Journal on Scientific Computing **23**, 1189-1203 (2001)

(with G. Benettin and A.M. Cherubini)

[19] **Stability properties of the Riemann ellipsoids
**Preprint-PS

Archive for Rational Mechanics and Analysis **158, **259-292 (2001)

(with D. Lewis)

[18] **Nekhoroshev-stability of L4 and L5 in
the spatial restricted three-body problem**

Regular and Chaotic Dynamics **3,
**56-72
(1998).

(with G. Benettin and M. Guzzo)

NOTE: For an editorial error, the
journal published a preliminary version of the article, which is
significantly different from the final version in a few points (including
some of the numerical results). The correct version of the article can
be downloaded from the web
page of the journal or else from here,
as a postscript file.

[17] **On the stability of elliptic equilibria
**Article-PS

MPEJ - Mathemathical Physics Electronic Journal
**4,
**Paper
1 (1998).

(with G. Benettin and M. Guzzo)

[16] **Compatibility of symplectic structures
adapted to noncommutatively integrable systems ** Preprint-PS

Journal of Geometry and Physics **27, **199-220
(1998).

(with T. Ratiu)

[15] **Nekhoroshev--stability of elliptic equilibria
of Hamiltonian systems** Preprint-PS

Communications in Mathematical Physics **197,
**347-360
(1998).

(with G. Benettin and M. Guzzo)

[14] **From Hamiltonian perturbation theory to
symplectic integrators and back ** Preprint-PS

Applied Numerical Mathematics **29, **73-87
(1999).

(with G. Benettin)

[13] **Fast rotations of the rigid body: A study
by Hamiltonian perturbation theory.**
**Part II: Gyroscopic rotations**

Nonlinearity **10,** 1695-1717 (1997)

(with G. Benettin and M. Guzzo)

[12] **On
the conservation of adiabatic invariants for a system of coupled rotators**

Physica D** 104,** 253--268 (1997)

(with G. Benettin and A. Carati)

[11] ** Fast rotations of the rigid body**

In *New trends in Hamiltonian Systems
and Celestial Mechanics*, J. Llibre e A. Lacomba ed.,

Advanced Series on Nonlinear Dynamics **8, **pag.
163-177 (World Scientific, Singapore, 1996).

[10] **Quasi--periodicity
of motions and complete integrability of Hamiltonian systems **Preprint-PS

Ergodic Theory and Dynamical Systems **18**,
1349-1362 (1998)

[9] **The Euler--Poinsot top: a non--commutatively
integrable system without global action--angle coordinates**

Journal of Applied Mathematics and Physics (ZAMP)
**47**,
953-976 (1996)

[8] **Fast rotations of the rigid body:
A study by Hamiltonian perturbation theory. Part I.**

Nonlinearity **9,** 137-186 (1996)

(with G. Benettin)

[7] ** Hamiltonian perturbation theory on
a manifold**

Celestial Mechanics and Dynamical Astronomy **
62,** 43-69 (1995)

[6] **Perturbation theory for systems without
global action--angle coordinates**

In *Hamiltonian Mechanics: Integrability and
Chaotic Behaviour*, J. Seimenis editor,

pg. 113-120 (Plenum, New York, 1994)

[5] ** Classical ``freezing'' of plane rotations:
a proof of the Boltzmann--Jeans conjecture**

Journal of Statistical Physics **63, **737-760
(1991)

(with G. Benettin)

[4] **Lie series method for vector fields
and Hamiltonian perturbation theory**

Journal of Applied Mathematics and Physics (ZAMP)
**41**,
843-864 (1990)

[3] **Exponential estimates on the one dimensional
Schroedinger equation with bounded analytic potential**

Annales de l'Institut Henri Poincare - Physique
theorique** 51,** 45-66 (1989)

(with G. Benettin and L. Chierchia)

[2] **On a relation among Lie series**

Celestial Mechanics and Dynamical Astronomy **
46,** 113-118 (1989)

[1] **Composition of Lie transforms with rigorous estimates and applications
to Hamiltonian**
**perturbation theory**

Journal of Applied Mathematics and Physics (ZAMP) **40,** 307-329
(1989)

(with G. Benettin)

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