# Jerzy Kijowski

# Hamiltonian dynamics, Kähler structures, asymptotic variables

** Abstract: **

The following theorem will be proved:
Given a convex Hamiltonian function on a classical
linear phase space (symplectic space), there is a unique
(almost) Kähler structure, such that:

1) the symplectic form is equal
to the imaginary part of the hermitean metric and

2) the Hamiltonian is given by a self-adjoint operator.

Physical examples are discussed. Example of the
field evolution at null-infinity (''on the SCRI"") is
discussed in detail.