Università di Padova - Dipartimento di Matematica Pura ed Applicata
Francesco FassÚ 

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 380 (2016), 3167-3172
(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 18, Issue 1 (2015)
(with D. Fontanari and D. Sadovskii)

[47] Conservation of  energy and momenta in nonholonomic systems with affine constraints   Preprint
Regular and Chaotic Dynamics  20 (2015), 449-462
(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 26 (2016), 519-544 (available as Online First)
(with N. Sansonetto)

[45] No monodromy in the champagne bottle, or singularities of a superintegrable system    Preprint
Journal of Geometric Mechanics
8 (2016), 375-389.
(with L. Bates)

[44] Quasi-periodicity in relative quasi-periodic tori.  Preprint
Nonlinearity 28 (2015) 4281-4301
(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 6, 1343-1355 (2009) 
(with N. Sansonetto)

[37] Gauge conservation laws and the momentum equation in nonholonomic mechanics.
Reports on Mathematical Physics 62, 345-367 (2008) Preprint - PDF 
(with A. Giacobbe and N. Sansonetto)

[36]  The exact computation of the free rigid body motion and its use in splitting methods.  Preprint - PDF 
Siam Journal on Scientific Computing 30, 2084-2112 (2008)
(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 12, 675-679 (2007) (Special issue dedicated to Richard Cushman)
(with L. Bates)

[34]  The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions Revised version - PDF 
Regular and Chaotic Dynamics 12, 579-588 (2007) (Special issue dedicated to Richard Cushman)
(with A. Ramos and N. Sansonetto)

[33]  Integrable almost--symplectic Hamiltonian systems Preprint - PDF 
Journal of Mathematical Physics 48, no. 9, 092902 (2007).
(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 3, article 051 (2007)
(with A. Giacobbe)

[31]  Geometry of KAM tori for nearly integrable Hamiltonian systems  Preprint - PDF 
Ergodic Theory and Dynamical Systems  27 (3),  725-741 (2007).
(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 87, 93-121 (2005) 
Preprint (revised version) -PS 

[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 44, 571-584 (2004)
(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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