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APPLIED MATHEMATICS SEMINAR ON 25 NOVEMBER 2004

Published on the 24 Nov 2004

APPLIED MATHEMATICS SEMINAR ON 25 NOVEMBER 2004

Completeness of the time-independent Hénon-Heiles Hamiltonians

  1. Date: Thursday, November 25
  2. Time: 11 a.m.
  3. Room: Red Centre 4082

We consider the cubic and quartic H'enon-Heiles Hamiltonians with additional inverse square terms,
which pass the Painlev'e test for only seven sets of coefficients.

For all the not yet integrated cases,
we prove the singlevaluedness of the general solution by building a birational transformation to two fourth order first degree
equations in the classification (Cosgrove, 2000) of such polynomial equations
which possess the Painlev'e property.

The seven Hamiltonians enjoy two properties:
meromorphy of the general solution, which is hyperelliptic with genus two,
and completeness in the Painlev'e sense
(impossibility to add any term to the Hamiltonian without destroying
the Painlev'e property).