Differential Equations and Dynamical Systems
The area of Differential Equations and Dynamical Systems distinguishes itself by the variety of publications of its members, many of them young, including the publication of books of the specialty. It continues pursuing research in its areas of expertise and to further develop bridges with other areas and with applications.
In particular, the members develop research in the following topics:
Differential Equations: nonlinear dispersive partial differential equations, including local and global well-posedness initial data with low regularity; singularities formation and stability of solitary waves; mathematical relativity and Einstein's equations, including study of the initial value problem and qualitative properties of solutions in the presence of black holes; variational problems and Morse theory, including variational methods in Hamiltonian mechanics and elliptic equations; stochastic differential equations, including variational problems and stochastic geometric mechanics.
Dynamical Systems: reaction-diffusion equations, including stability, bifurcations and pattern formation; qualitative theory of functional equations, including stability, bifurcation and oscillatory behavior; ergodic theory and nonuniform hyperbolicity; dynamics in infinite dimensions, including hyperbolicity and Morse-Smale property for delay equations and evolution equations; topological dynamics, kneading theory, topological invariants, Bowen-Franks groups and zeta functions; integrability and nonintegrability of equations of mathematical physics; Hamiltonian systems, including stability and bifurcation of relative equilibria.