  Phase-space partitioning offers an attractive path for the precise tailoring
of complex dynamical systems. In Beam Physics, the proposed approach involves
(i) producing beams with cross-plane correlations to control kinematical
invariants known as eigenemittances and (ii) mapping them to invariants of
motion associated with given degrees of freedom via a decoupling
transformation. Here we report on the direct experimental demonstration of the
mapping of eigenemittances to transverse emittances for an electron beam.
Measured phase space density confirms the generation of beams with asymmetric
transverse emittance ratio> 200 consistent with the initiated eigenemittance
values. The results could have broad applications to other fields where
invariants are sometimes used to describe coupled classical system quantum
systems with mixed states.
