Roberta Fabbri's Homepage

foto robi

Permanent Address: Dipartimento di Matematica e Infomatica "Ulisse Dini" (from 01/01/2013)
                                   Dipartimento di Sistemi e Informatica (1/11/2000-31/12/2012)
                                   Universita' di Firenze
                                   Ufficio: Via Santa Marta, 3
                                   500139 Firenze
                                   tel. +390554796496
                                   fax +390554796363

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.


Didactic duties

academic year 2013/14    Esercizi di riepilogo Ing Informatica 2013-14
                                          Registro lezioni 2013-14
academic year 2012/13   Esercizi riepilogo Ing Informatica 2012-13
                                         Registro lezioni 2012-13


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.

23 R. Fabbri, R. Johnson, S. Novo, C. Núñez, "Some remarks concerning weakly disconjugate linear nonautonomous Hamiltonian systems", Journal of Mathematical Analysis and Applications, 380, (2011), pp. 853-864.

24 R. Fabbri, R. Johnson, S. Novo, C. Núñez, "On linear-quadratic dissipative control processes with time-varying coefficients", Discrete and Continuous Dynamical Systems - Series A, vol. 33, Issue 1, January 2013, pp. 193-210.

25 R. Fabbri, C. Elia, "Rotation number and exponential dichotomy for linear Hamiltonian systems: from theoretical to numerical aspects", Journal of Dynamics and Differential Equations, vol. 25, Issue 1, (2013), pp. 95-120.

Book Chapters

26 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.

27 R. Fabbri, "The relation between dynamics and the spectrum of one-dimensional Schrödinger operator", Mathematisches Forschungsinstitut Oberwolfach, Report No. 51/2005 pp. 2947—2949.

28 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.


29  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

30 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.  

31  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.


32  R. Fabbri, R. Johnson, S. Novo, C. Núñez, R. Obaya  "Oscillation Theory for Hamiltonian Systems", in preparation.

Organized Activities