Dipartimento di Sistemi e Informatica Applied Mathematics Research Group 
Resp. Prof. R. Johnson
The Applied Mathematics
Group carries out research on a wide range of problems in the area of differential
equations and dynamical systems with particular emphasis on their role in
applied situations. Many of these problems concern the properties of solutions
of nonautonomous differential equations, where it is understood that such
equations are studied using tools of ergodic theory and topological dynamics
(such as Lyapunov exponents, exponential dichotomies, and rotation numbers),
together with more classical methods such as the topological degree (when
the timedependence happens to be periodic). Some specific themes that have
been taken up by the Applied Mathematics Group in the last three years and
which are still under active study are the following.
1.Problems of homoclinic bifurcation in singularly perturbed differential
equations; these are studied using the exponential dichotomy method.
2.Periodically driven partial differential equations in thin domains, including
the NavierStokes equations; these are studied using the topological degree.
3.Sliding mode control problems; among various methods we use the topological
degree.
4.Random bifurcation theory, with particular emphasis on a random version
of the Duffingvan der Pol oscillator.
5.Spectral theory of random differential operators, in particular the Cantor
spectrum problem for the quasiperiodic Schroedinger operator.
6.Control theory of randomly driven systems.
7.Random polynomials, with special emphasis on a class of these polynomials
which can be described using the classical theory of algebraic curves.
The Group collaborates with colleagues from the following universities: (Italy) Ancona, Milano, Siena; (foreign) Valladolid (Spain), Georgia Tech (USA), Rutgers (USA). The members of the Group at the present time are: R. Johnson (professor), R. Fabbri (postdoctoral researcher), F. Mantellini (doctoral student), E. Zoli (doctoral student).
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