- complex analysis,
- moduli spaces,
- Lie groups and geometric group theory,
- spectral theory.
Results in one domain can imply important corollaries in the other ones. For example, dynamical properties of polygonal billiards are related to the Teichmüller flow and geometry of the moduli spaces. The Hilbert 16-th problem is related to holomorphic foliations, complex geometry and analysis, algebraic geometry. Modern complex dynamics is on the bridge between two domains: the classical theory of dynamical systems and complex (algebraic) geometry.
The special year of dynamical systems is intended to bring together specialists working in the above-mentioned areas, which would enrich everybody.