Roberta Fabbri's Homepage
Permanent Address: Dipartimento
di Sistemi e Infomatica
Facolta' di Ingegneria
Universita' di Firenze
Via Santa Marta, 3
500139 Firenze
tel. +390554796356
fax +390554796363
e-mail fabbri@dsi.unifi.it
Position :
Assistant Professor (Ricercatore) since November 1st, 2000
Research interests :
Nonautonomous Dynamical Systems, Quasi periodic Schrödinger
operator (continuous and discrete case). Spectral properties, Cantor
spectrum.
Exponential dichotmoy, rotation number for linear nonautonomous
Hamiltonian systems. Control theory . Bifurcation theory for
nonautonomous systems.
My
CV: (in Italian)
CURRICULUM ATTIVITA SCIENTIFICA E
DIDATTICA
References:
1. R. Fabbri, "Genericita’ dell’Iperbolicita’ nei sistemi differenziali
lineari di dimensione due", Boll. U.M.I: 1-A Suppl. (1998)
2. R. Fabbri, R. Johnson, "On the Lyapunov exponent of certain SL(2,
R)-valued cocycles", Differential Equations and Dynamical Systems 7 (3)
(1999), pp. 349-370.FJ1
3. R. Fabbri, R. Johnson, "Genericity of exponential dichotomy for
two-dimensional differential systems”, Annali di Matematica Pura e
Applicata, 178 (2000), pp.175-193.
4. R. Fabbri, R. Johnson, R. Pavani, "On the nature of the spectrum of
the quasi-periodic Schrödinger operator", Nonlinear Analysis: RWA
3 (2001), pp. 37-59.
5. R. Fabbri, R. Johnson, "On Quasi-Sections to Locally Free Circle
Actions", Atti Sem. Mat. Fis. Univ. Modena 49
(2001), pp. 307-317.
6. R. Fabbri, "On the Lyapunov exponent and exponential dichotomy
for the quasi-periodic Schrödinger operator", Bollettino U.M.I. 5
(2002), pp. 149-161.
7 R. Fabbri, R. Johnson, C. Núñez, "Rotation number for
non-autonomous linear Hamiltonian systems I: Basic properties",
Zeit. Angew. Math. Phis., 54, (2003), pp. 484-502.
8 R. Fabbri, R. Johnson, C. Núñez, "Rotation number for
non-autonomous linear Hamiltonian systems II: the Floquet coefficient",
Zeit. Angew. Math. Phis., 54, (2003), pp. 652-676.
9 R. Fabbri, R. Johnson, C. Núñez, "On the
Yakubovich Frequency Theorem for Linear Non- Autonomous Control
Processes", Discrete and Continuous Dynamical Systems, vol. 9, 3,
(2003),
pp.677-704
10 R. Fabbri, F. Colonius, "Controllability for systems with
slowly varying parameters” ESAIM: Control, Optimization and
Calculus of Variations, 9 (2003), pp. 207-216.
11 R. Fabbri, S. Impram, R. Johsnon, "On a criterion of Yakubovich type
for the absolute stability of nonautonomous control
processes”, Inter. Jour. Math. and Math. Sciences 16 (2003),
pp.1027-1042.
12 R. Fabbri, R. Johnson, P.Kloeden, "Digitization of nonautonomous
control processes", Jour. Diff. Eqns. 195 (2003), pp. 210-229;
reprinted in Jour. Diff. Eqns. 208 (Special Issue 2005),
pp. 509-529.
13 R. Fabbri, R. Johnson, F. Mantellini, "A non-autonomous saddle-node
bifurcation pattern", Stochastics and Dynamics,
vol. 4, 3, (2004), pp.
335-350.
14 R. Fabbri, C. Núñez, A. Sanz, "A perturbation
theorem for linear Hamiltonian systems with
bounded orbits", Discrete and Continuous Dynamical Systems, vol.
13, 3, (2005), pp. 623-635.
15. R. Fabbri, T. Jäger, R. Johnson, G. Keller, "A
Sharkovskii-type theorem for minimally forced interval
maps", Topological Methods in Nonlinear Analysis, vol. 26, (2005), pp.
163-188
.
16.R. Fabbri, R. Johnson, C. Núñez, "Disconjugacy and the
rotation number for linear, non- autonomous Hamiltonian systems",
Annali di Matematica Pura ed Applicata, vol. 185, 5, (2006), pp. 3-21.
17.F. Colonius, R. Fabbri, R. Johnson, "On non-autonomous H^\infty
control with infinite horizon", Journal Differential Equations,
220, (2006), pp. 46-67
18 F. Colonius, R. Fabbri, R. Johnson, "Chain Recurrence, Growth rates
and Ergodic Limits", Ergodic Theory and Dynamical Systems, vol.
27, Issue 05, (2007), pp. 1509-1524.
19 R. Fabbri, R. Johnson, K. Palmer, "Another look at averaging and
integral manifolds", Jour. Difference Eqns. Appl., vol. 13, Issue 8-9,
August 2007, pp. 723-739.
20 F.Colonius, R. Fabbri, R. Johnson, M. Spadini, "Bifurcation
Phenomena in Control Flows", Topological Methods in Nonlinear Analysis,
vol. 30, (2007), pp. 87-111.
21 Nguyen Dinh Cong, R. Fabbri, "On the spectrum of the one-dimensional
Schrödinger operator" , Discrete and Continuous Dynamical Systems
B, vol. 9, num. 3 & 4. May & June 2008, pp. 541-554.
22 R. Fabbri, R. Johnson, L. Zampogni, "On the Lyapunov Exponent of
certain SL(2, R)-Valued Cocycles II", Differential Equations and
Dynamical Systems, Vol. 18, Nos. 1 & 2, January & April
2010, pp. 135-161.
Book Chapters
23 R. Fabbri, R. Johnson, C. Núñez, "On the Frequency
Theorem for nonperiodic systems", Dynamics, Bifurcations and Control,
F. Colonius, L. Gruene (Eds),
Lecture Notes in Control and Information Sciences 273,
Springer-Verlag 2002, pp. 233-240.
24 R. Fabbri, "The relation between dynamics and the spectrum of
one-dimensional Schrödinger operator", Mathematisches
Forschungsinstitut Oberwolfach, Report No. 51/2005 pp. 2947—2949.
25 R. Fabbri, R. Johnson, L. Zampogni, "Nonautonomous differential
systems in two dimension", Handbook of Differential Equations: Ordinary
Differential Equations, Vol. 4, eds. F.Battelli, M. Feckan, Elsevier
Publishing, Amsterdam 2008, pp. 135-268.
Proceedings
26 R. Fabbri, R. Johnson, C. Núñez, "Rotation
number and disconjugacy for linear, time-dependent hamiltonian
systems", Actas del 18^ Congreso de Ecuaciones Diferenciales y
Aplicaciones, Taragona (Espana), 15-19 septiembre 2003, CD-ROM
27 R. Fabbri, R. Johnson. "On a saddle-node bifurcation in a problem of
quasi-periodic harmonic forcing", Proceedings EQUADIFF 2003, World Sci.
Publ. Hackensack, NJ, 2005, pp. 839-847.
28 R.Fabbri, R. Johnson, "Exponential dichotomies and a nonlinear
H^\infty control problem", Applied and
Industrial Mathematics in Italy, Series on Advances in Mathematics for
Applied Sciences,
69, World Sci. Publ, NJ, 2005, pp. 315-323.
Books
29 R. Fabbri, R. Johnson, S. Novo, C. Núñez, R.
Obaya "Oscillation Theory for Hamiltonian Systems", in
preparation.
Organized Activities