### Mathematics & Mechanics Faculty

#### Differential Equations department

#### The Head of the Department - professor V.A.Pliss

##### Domains of research

- - structural stability, stability with respect
to arbitrary C
^{0}-small and C - small perturbations.
(V.A.Pliss, S.Yu.Pilyugin);
- - structure of invariant sets, integral manifolds, attractors.
(V.A.Pliss, S.Yu.Pilyugin, Yu.A.Il'in);
- - bifurcations of invariant sets with complicated structure.
(Yu.N.Bibikov, V.E.Chernyshev, Yu.V.Churin);
- - qualitative theory in the plane (A.F.Andreyev, A.V.Osipov);
- - applications to mathematical models in biology, numerical methods for qualitative investigation of dynamical systems (A.V.Osipov, S.Yu.Pilyugin, V.V.Vinogradov).
- - linear systems of differential equations (L.Ya.Adrianova).

#### Monographs

*
*- 1. V.A.Pliss. Nonlocal Problems of the Theory of Oscillations. Academic Press, 1966.
- 2. Yu.N.Bibikov. Local Theory of Non-Linear Analytic Ordinary
Differential Equations. Lect. Notes in Math., v.702, Springer, 1979.
- 3. S.Yu.Pilyugin. Introduction to Structurally Stable Systems of Differential Equations. Birkhauser, 1992.
- 4. S.Yu.Pilyugin. The Space of Dynamical Systems with C -Topology.
Lect. Notes in Math.,v.1571, Springer,1994.
* 5. L.Ya.Adrianova. Introduction to Linear Systems of Differential Equations. Amer. Math. Soc., 1995.
*