CURRICULUM VITAE. Homepage: Nationality. Italian. Current position. Full Professor of Mathematical Physics

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1 CURRICULUM VITAE Professor Maria Letizia Bertotti Faculty of Science and Technology Free University of Bozen - Bolzano Via Leonardo da Vinci Bolzano ITALY Phone: Fax: MariaLetizia.Bertotti@unibz.it Homepage: Nationality Italian Current position Full Professor of Mathematical Physics Education 1982, Laurea in Mathematics, University of Trento. 1985, Degree of Magister Philosophiae in Mathematical Physics, S.I.S.S.A., Trieste. Academic positions 18/06/ /10/1998: Assistant Professor (Mathematical Physics) at the Faculty of Science of the University of Trento; 01/11/ /10/2000: Associate Professor (Mathematical Analysis) at the Faculty of Engineering of the University of Palermo; 01/11/ /10/2008: Full Professor (Mathematical Physics) at the Faculty of Engineering of the University of Palermo; Since 01/11/2008: Full Professor (Mathematical Physics) at the Faculty of Science and Technology of the Free University of Bozen-Bolzano. Didactic experience

2 Experience spanned over more than twenty years, teaching courses in Mathematical Analysis (I, II and Complements), Rational Mechanics, Mathematical Physics, Mathematical Models, at various levels at the Universities of Trento (Faculty of Sciences and Faculty of Engineering), Palermo (Faculty of Engineering) and Bolzano (Faculty of Science and Technology). Research activity Fields of interest: Dynamical Systems Hamiltonian Systems Nonlinear Analysis Mathematical Models Complex Systems My research activity is concerned with nonlinear dynamics and differential equations arising in different fields. In past years it has been mainly devoted to the study of classical mechanics problems described by Lagrangian and Hamiltonian systems: it has been addressed to qualitative aspects of the dynamics and to the search of periodic, homoclinic and heteroclinic solutions. In these investigations, in particular, variational methods of the critical point theory play a great role. Three selected publications pertaining to this area are: M.L. Bertotti, Forced Oscillations for Singular Dynamical Systems with an Application to the Restricted Three Body Problem, Journal of Differential Equations, vol. 93, pp , (1991). M.L. Bertotti - S.V. Bolotin, Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields, Annali di Matematica Pura ed Applicata, (IV), vol. CLXXIV, pp , (1998). M.L. Bertotti - S.V. Bolotin, On the influence of the kinetic energy on the stability of equilibria of natural Lagrangian systems, Archive for Rational Mechanics and Analysis, vol. 152, pp , (2000). More recently, my interest was captured by complex systems arising in different applied sciences, with a special focus on social and economical ones. In several problems belonging to these fields one deals with systems composed by a high number of interacting units characterized by some non mechanical variable (the so called activity), which expresses a social or economical state, as e.g. wealth, religion, political ideas, opinions on some issue. The goal is to try to explain

3 emerging collective behaviors and macroscopic social features as a result of microscopic, namely individual, interactions. In this connection, the attempt can be done to describe the evolution in time of a distribution function over the activity variable of the community under consideration. The subsequent step is of course to study the dynamics defined by the resulting evolution equations. It s worth while mentioning that these topics are presently attracting a growing and keen attention among the scientific community. My approach comprises various aspects, including the development of a modelling strategy (introduction of a general framework inspired to the mathematical kinetic theory and expressed by a system of ordinary differential equations or also partial differential equations) within which formulating single models, the construction of specific models and their analytical study (performed with tools from nonlinear analysis and dynamical systems theory), possibly combined with some computational simulations. Three recent publications in this direction are: M.L. Bertotti M. Delitala, On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders, Mathematical Models & Methods in Applied Sciences, vol. 18, nr. 6, pp , (2008). M.L. Bertotti, On a class of dynamical systems with emerging cluster structure, Journal of Differential Equations, vol. 249, pp , (2010). M.L. Bertotti G. Modanese, From microscopic taxation and redistribution models to macroscopic income distributions, Physica A, vol. 390, pp , (2011).

4 Selected Publications Articles in International Refereed Journals * M.L. Bertotti G. Modanese, Exploiting the flexibility of a family of models or taxation and redistribution, European Physical Journal B, vol. 85, nr. 8, 261, (2012); * M.L. Bertotti G. Modanese, From microscopic taxation and redistribution models to macroscopic income distributions, Physica A, vol. 390, pp , (2011); * M.L. Bertotti, From individual interactions to collective patterns. A mathematical approach, Advances and Applications in Statistical Sciences, vol. 6, pp , (2011); * M.L. Bertotti, Modelling taxation and redistribution: a discrete active particle kinetic approach, Applied Mathematics and Computation, vol. 217, nr. 2, pp , (2010); * M.L. Bertotti, On a class of dynamical systems with emerging cluster structure, Journal of Differential Equations, vol. 249, pp , (2010); * M.L. Bertotti M. Delitala, Cluster formation in opinion dynamics: a qualitative analysis, Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP), vol. 61, nr. 4, pp , (2010); * M.L. Bertotti - M. Delitala, On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders, Mathematical Models & Methods in Applied Sciences, vol. 18, nr. 6, pp , (2008); * M.L. Bertotti - M. Delitala, On a discrete kinetic approach for modelling persuaders influence in opinion formation processes, Mathematical and Computer Modelling, vol. 48, pp , (2008); * M.L. Bertotti - M. Delitala, Conservation laws and asymptotic behavior of a model of social dynamics, Nonlinear Analysis: Real World Applications, vol. 9, pp , (2008); * N. Bellomo - M.L. Bertotti - M. Delitala, From the kinetic theory of active particles to the modelling of social behaviors and politics, Quality and Quantity, vol. 41, nr. 4, pp , (2007);

5 * M.L. Bertotti - M. Delitala, On the qualitative analysis of the solutions of a mathematical model of social dynamics, Applied Mathematics Letters, vol. 19, pp , (2006); * M.L. Bertotti - M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Mathematical Models & Methods in Applied Sciences, vol. 14, nr. 7, pp , (2004); * M.L. Bertotti - N. Bellomo, Boundary value steady solutions of a class of hydrodynamic models for vehicular traffic flow, Mathematical and Computer Modelling, vol. 38, nr. 3-4, pp , (2003); * M.L. Bertotti - S.V. Bolotin, Chaotic trajectories for natural systems on a torus, Discrete and Continuous Dynamical Systems, Series A, vol. 9, nr. 5, pp , (2003); * M.L. Bertotti - S.V. Bolotin, On the influence of the kinetic energy on the stability of equilibria of natural Lagrangian systems, Archive for Rational Mechanics and Analysis, vol. 152, pp , (2000); * F. Alessio - M.L. Bertotti - P. Montecchiari, Multibump solutions to possibly degenerate equilibria of almost periodic Lagrangian systems, Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP), vol. 50, n. 6, pp , (1999); * M.L. Bertotti - P. Montecchiari, Connecting orbits for some classes of almost periodic Lagrangian systems, Journal of Differential Equations, vol. 145, pp , (1998); * M.L. Bertotti - S.V. Bolotin, Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields, Annali di Matematica Pura ed Applicata, (IV), vol. CLXXIV, pp , (1998); * M.L. Bertotti - S.V. Bolotin, Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff, Rendiconti Lincei: Matematica e Applicazioni, serie IX, vol. VIII, pp , (1997); * M.L. Bertotti - L. Jeanjean, Multiplicity of homoclinic solutions for singular second order conservative systems, Proceedings of the Royal Society of Edinburgh, vol. 126A, pp , (1996); * M.L. Bertotti - S.V. Bolotin, A variational approach for homoclinics in almost periodic Hamiltonian systems, Communications on Applied Nonlinear Analysis, vol. 2, pp , (1995);

6 * M.L. Bertotti - S.V. Bolotin, Homoclinic solutions of quasiperiodic Lagrangian systems, Differential and Integral Equations, vol. 8, pp , (1995); * M.L. Bertotti, Homoclinics for Lagrangian systems on Riemannian manifolds, Dynamic Systems and Applications, vol. 1, pp , (1992); * M.L. Bertotti, Forced oscillations for singular dynamical systems with an application to the restricted three body problem, Journal of Differential Equations, vol. 93, pp , (1991); * M.L. Bertotti, Multiplicity of kt-periodic solutions near a given T-periodic solution for nonlinear Hamiltonian systems, Differential and Integral Equations, vol. 2, pp , (1989); * M.L. Bertotti, Multiplicity of subharmonic solutions of forced Hamiltonain systems near an equilibrium, Manuscripta Mathematica, vol. 64, pp , (1989); * M.L. Bertotti, Localization of closed orbits of nonlinear Hamiltonian systems with 1:-2 resonance near an equilibrium, Bollettino Unione Matematica Italiana, vol. 7 (1B), pp , (1987); * M.L. Bertotti, Forced oscillations of asymptotically linear Hamiltonian systems, Bollettino Unione Matematica Italiana, vol. 7 (1B), pp , (1987); * M.L. Bertotti - V. Moauro, Bifurcation and total stability, Rendiconti del Seminario Matematico dell'università di Padova, vol. 71, pp , (1984); Contributions to Books * A. Ambrosetti - M.L. Bertotti, Homoclinics for second order conservative systems, Partial Differential Equations and Related Subjects, volume in onore di Louis Niremberg, M. Miranda ed., Pitman Research Notes in Mathematics, Longman Scientific & Technical, pp , (1992); * M.L. Bertotti, A note on a Theorem of Conley and Zehnder, Recent advances in Hamiltonian systems, G.F. Dell'Antonio e B.M. D'Onofrio ed., World Scientific, pp , (1987);

7 * M.L. Bertotti - E. Zehnder, A Poincaré-Birkhoff type result in higher dimensions, Stochastic processes in classical and quantum systems, S. Albeverio, G. Casati e D. Merlini ed., Lecture Notes in Physics 262, Springer Verlag, pp , (1986);

8 CURRICULUM VITAE Prof.ssa Maria Letizia Bertotti Facoltà di Scienze e Tecnologie Libera Università di Bolzano Via Leonardo da Vinci Bolzano Telefono: Fax: MariaLetizia.Bertotti@unibz.it Homepage: Nazionalità Italiana Posizione attuale Professore Ordinario di Fisica Matematica (MAT07) Formazione/studi 1982, Laurea in Matematica, Università degli Studi di Trento. 1985, Diploma di Perferzionamento Magister Philosophiae in Fisica Matematica, S.I.S.S.A., Trieste. Posizioni ricoperte 18/06/ /10/1998: Ricercatore Universitario nel SSD Fisica Matematica presso la Facoltà di Scienze Matematiche, Fisiche e Naturali della Università degli Studi di Trento. 01/11/ /10/2000: Professore Associato nel SSD Analisi Matematica presso la Facoltà di Ingegneria dell Università degli Studi di Palermo. 01/11/200 31/10/2008: Professore Ordinario nel SSD Fisica Matematica presso la Facoltà di Ingegneria dell Università degli Studi di Palermo. Dallo 01/11/2008 a tutt oggi: Professore Ordinario nel SSD Fisica Matematica presso la Facoltà di Scienze e Tecnologie della Libera Università di Bolzano. Esperienza didattica

9 Estesa e diversificata esperienza didattica, comprendente insegnamenti di Analisi Matematica (I, II e Complementi), Meccanica Razionale, Fisica Matematica, Modelli Matematici, presso diversi corsi di laurea della Facoltà di Scienze Matematiche, Fisiche e Naturali e della Facoltà di Ingegneria dell Università degli Studi di Trento, della Facoltà di Ingegneria dell Università degli Studi di Palermo e della Facoltà di Scienze e Tecnologie della Libera Università di Bolzano. Attività di ricerca Aree di interesse: Sistemi Dinamici Sistemi Hamiltoniani Analisi Nonlineare Modelli Matematici Sistemi Complessi Denominatore comune dei problemi oggetto delle mie ricerche è il fatto che essi riguardano la dinamica di sistemi di equazioni nonlineari di interesse nelle applicazioni. In passato mi sono occupata essenzialmente di sistemi della meccanica classica ad un numero finito di gradi di libertà, descritti da equazioni di Lagrange o di Hamilton. L obiettivo era quello di studiare proprietà qualitative della relativa dinamica, e in particolare provare l esistenza di soluzioni periodiche, omocline od eterocline. Le tecniche e gli strumenti impiegati appartengono all analisi nonlineare e, in particolare, alla teoria dei punti critici. I problemi si riconducono infatti alla ricerca di punti stazionari di opportuni funzionali possibilmente non limitati. Tre pubblicazioni scelte fra quelle pertinenti a questo filone sono: M.L. Bertotti, Forced Oscillations for Singular Dynamical Systems with an Application to the Restricted Three Body Problem, Journal of Differential Equations, vol. 93, pp , (1991). M.L. Bertotti - S.V. Bolotin, Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields, Annali di Matematica Pura ed Applicata, (IV), vol. CLXXIV, pp , (1998). M.L. Bertotti - S.V. Bolotin, On the influence of the kinetic energy on the stability of equilibria of natural Lagrangian systems, Archive for Rational Mechanics and Analysis, vol. 152, pp , (2000).

10 Più recentemente, il mio interesse si è andato focalizzando su sistemi complessi che si incontrano in campi diversi, con particolare riguardo a questioni del campo delle scienze sociali ed economiche. In parecchi problemi tipici di tali contesti, si ha a che fare con sistemi composti da un elevato numero di individui, caratterizzati da una variabile (eventualmente a valori vettoriali) non meccanica (chiamata attività), che esprime uno stato economico o sociale, per esempio la ricchezza, la religione, le idee politiche, l opinione in merito ad un determinato argomento. Ci si prefigge di spiegare comportamenti collettivi emergenti e caratteristiche sociali di tipo macroscopico in base alle (vale a dire, come conseguenza delle) interazioni microscopiche, cioè individuali. All uopo, così come nella teoria cinetica dei gas, si può pensare di descrivere e modellare l evoluzione temporale di una funzione di distribuzione sulla variabile attività della comunità sotto studio. Una volta costruito il modello, il passo successivo consiste ovviamente nello studio della dinamica delle equazioni cui si perviene. Vale la pena osservare che simili argomenti sono oggetto di un attenzione via via crescente nella comunità scientifica. Il mio approccio comprende vari aspetti, che vanno dallo sviluppo di un framework generale (ispirato ad una opportuna discretizzazione della teoria cinetica ed espresso mediante un sistema di equazioni differenziali ordinarie, o anche a derivate parziali), entro il quale formulare poi i singoli modelli, alla costruzione di modelli specifici ed al loro studio analitico (condotto con strumenti dell analisi nonlineare e della teoria dei sistemi dinamici), integrato e corredato da simulazioni computazionali. Tre pubblicazioni recenti appartenenti a questo filone di ricerca sono: M.L. Bertotti M. Delitala, On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders, Mathematical Models & Methods in Applied Sciences, vol. 18, nr. 6, pp , (2008). M.L. Bertotti, On a class of dynamical systems with emerging cluster structure, Journal of Differential Equations, vol. 249, pp , (2010). M.L. Bertotti G. Modanese, From microscopic taxation and redistribution models to macroscopic income distributions, Physica A, vol. 390, pp , (2011).

11 Pubblicazioni scelte Articoli in Riviste Internazionali con Referee * M.L. Bertotti G. Modanese, Exploiting the flexibility of a family of models or taxation and redistribution, European Physical Journal B, vol. 85, nr. 8, 261, (2012); * M.L. Bertotti G. Modanese, From microscopic taxation and redistribution models to macroscopic income distributions, Physica A, vol. 390, pp , (2011); * M.L. Bertotti, From individual interactions to collective patterns. A mathematical approach, Advances and Applications in Statistical Sciences, vol. 6, pp , (2011); * M.L. Bertotti, Modelling taxation and redistribution: a discrete active particle kinetic approach, Applied Mathematics and Computation, vol. 217, nr. 2, pp , (2010); * M.L. Bertotti, On a class of dynamical systems with emerging cluster structure, Journal of Differential Equations, vol. 249, pp , (2010); * M.L. Bertotti M. Delitala, Cluster formation in opinion dynamics: a qualitative analysis, Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP), vol. 61, nr. 4, pp , (2010); * M.L. Bertotti - M. Delitala, On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders, Mathematical Models & Methods in Applied Sciences, vol. 18, nr. 6, pp , (2008); * M.L. Bertotti - M. Delitala, On a discrete kinetic approach for modelling persuaders influence in opinion formation processes, Mathematical and Computer Modelling, vol. 48, pp , (2008); * M.L. Bertotti - M. Delitala, Conservation laws and asymptotic behavior of a model of social dynamics, Nonlinear Analysis: Real World Applications, vol. 9, pp , (2008); * N. Bellomo - M.L. Bertotti - M. Delitala, From the kinetic theory of active particles to the modelling of social behaviors and politics, Quality and Quantity, vol. 41, nr. 4, pp , (2007);

12 * M.L. Bertotti - M. Delitala, On the qualitative analysis of the solutions of a mathematical model of social dynamics, Applied Mathematics Letters, vol. 19, pp , (2006); * M.L. Bertotti - M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Mathematical Models & Methods in Applied Sciences, vol. 14, nr. 7, pp , (2004); * M.L. Bertotti - N. Bellomo, Boundary value steady solutions of a class of hydrodynamic models for vehicular traffic flow, Mathematical and Computer Modelling, vol. 38, nr. 3-4, pp , (2003); * M.L. Bertotti - S.V. Bolotin, Chaotic trajectories for natural systems on a torus, Discrete and Continuous Dynamical Systems, Series A, vol. 9, nr. 5, pp , (2003); * M.L. Bertotti - S.V. Bolotin, On the influence of the kinetic energy on the stability of equilibria of natural Lagrangian systems, Archive for Rational Mechanics and Analysis, vol. 152, pp , (2000); * F. Alessio - M.L. Bertotti - P. Montecchiari, Multibump solutions to possibly degenerate equilibria of almost periodic Lagrangian systems, Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP), vol. 50, n. 6, pp , (1999); * M.L. Bertotti - P. Montecchiari, Connecting orbits for some classes of almost periodic Lagrangian systems, Journal of Differential Equations, vol. 145, pp , (1998); * M.L. Bertotti - S.V. Bolotin, Doubly asymptotic trajectories of Lagrangian systems in homogeneous force fields, Annali di Matematica Pura ed Applicata, (IV), vol. CLXXIV, pp , (1998); * M.L. Bertotti - S.V. Bolotin, Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff, Rendiconti Lincei: Matematica e Applicazioni, serie IX, vol. VIII, pp , (1997); * M.L. Bertotti - L. Jeanjean, Multiplicity of homoclinic solutions for singular second order conservative systems, Proceedings of the Royal Society of Edinburgh, vol. 126A, pp , (1996); * M.L. Bertotti - S.V. Bolotin, A variational approach for homoclinics in almost periodic Hamiltonian systems, Communications on Applied Nonlinear Analysis, vol. 2, pp , (1995);

13 * M.L. Bertotti - S.V. Bolotin, Homoclinic solutions of quasiperiodic Lagrangian systems, Differential and Integral Equations, vol. 8, pp , (1995); * M.L. Bertotti, Homoclinics for Lagrangian systems on Riemannian manifolds, Dynamic Systems and Applications, vol. 1, pp , (1992); * M.L. Bertotti, Forced oscillations for singular dynamical systems with an application to the restricted three body problem, Journal of Differential Equations, vol. 93, pp , (1991); * M.L. Bertotti, Multiplicity of kt-periodic solutions near a given T-periodic solution for nonlinear Hamiltonian systems, Differential and Integral Equations, vol. 2, pp , (1989); * M.L. Bertotti, Multiplicity of subharmonic solutions of forced Hamiltonain systems near an equilibrium, Manuscripta Mathematica, vol. 64, pp , (1989); * M.L. Bertotti, Localization of closed orbits of nonlinear Hamiltonian systems with 1:-2 resonance near an equilibrium, Bollettino Unione Matematica Italiana, vol. 7 (1B), pp , (1987); * M.L. Bertotti, Forced oscillations of asymptotically linear Hamiltonian systems, Bollettino Unione Matematica Italiana, vol. 7 (1B), pp , (1987); * M.L. Bertotti - V. Moauro, Bifurcation and total stability, Rendiconti del Seminario Matematico dell'università di Padova, vol. 71, pp , (1984); Contributi a Libri * A. Ambrosetti - M.L. Bertotti, Homoclinics for second order conservative systems, Partial Differential Equations and Related Subjects, volume in onore di Louis Niremberg, M. Miranda ed., Pitman Research Notes in Mathematics, Longman Scientific & Technical, pp , (1992); * M.L. Bertotti, A note on a Theorem of Conley and Zehnder, Recent advances in Hamiltonian systems, G.F. Dell'Antonio e B.M. D'Onofrio ed., World Scientific, pp , (1987);

14 * M.L. Bertotti - E. Zehnder, A Poincaré-Birkhoff type result in higher dimensions, Stochastic processes in classical and quantum systems, S. Albeverio, G. Casati e D. Merlini ed., Lecture Notes in Physics 262, Springer Verlag, pp , (1986);