- 93-140 MacKay RS , Muldoon MR
- Diffusing through spectres: ridge curves, ghost circles
and a partition of phase space.
May 18, 93
(auto. generated ps),
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Abstract. The study of transport in Hamiltonian and related systems is greatly
illuminated if one can construct a
framework of ``almost invariant'' surfaces to organize the dynamics.
This can be done in the case of area-preserving twist maps, using
pieces of the stable and unstable manifolds of periodic
orbits or cantori, as shown by MacKay, Meiss and Percival. The
resulting surfaces are not, however, necessarily the most
appropriate ones, as they need not be graphs, nor is it clear
that they can always be chosen mutually disjoint. G.~R.~Hall
proposed a choice based on ``ridge curves'' for the gradient
flow of the associated variational problem, which C.~Gol\'e
christened ``ghost circles''. They have the advantage that they
are always graphs. In this letter, we present numerical experiments
suggesting that ghost circles are mutually disjoint.
Our work has subsequently led to a proof of this by Angenent
and Gol\'e. We propose that ghost circles form a convenient,
natural skeleton around which to organize studies of transport.