We consider 2D hydrodynamics of ideal fluid with free surface. A
time-dependent conformal transformation is used which maps a free
fluid surface into the real line with fluid domain mapped into the
lower complex half-plane. 2D fluid dynamics is fully characterized
by the complex singularities in the upper complex half-plane for the
time-dependent conformal transformation and the complex velocity.
These singularities are branch points approaching the fluid surface
as wavebreaking develops. We use the additional conformal
transformation to resolve the dynamics near branch points which
allows to analyze wavebreaking in details. We observed the formation
of multiple Crapper capillary solutions during overturning of the
wave.