| Abstract |
|
Consider the polynomial differential equation in \(\mathbb{C}^2\):
\(dz/dt = P(z,w)\), \(dw/dt=Q(z,w)\). The polynomials \(P\) and \(Q\)
are holomorphic, the time is complex. In order to study the global
behavior of the solutions, it is convenient to consider the extension
as a foliation in the projective plane.
I will discuss some recent results around the following questions. What is the ergodic theory of such systems? How do the leaves distribute in a generic case? |
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