- 99-200 Juan J. Abad, Hans Koch
- Renormalization and Periodic Orbits for Hamiltonian Flows
(109K, plain TeX, one eps figure)
May 28, 99
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Abstract. We consider a renormalization group transformation R
for analytic Hamiltonians in two or more dimensions,
and use this transformation to construct invariant tori,
as well as sequences of periodic orbits
with rotation vectors approaching that of the invariant torus.
The construction of periodic and quasiperiodic orbits
is limited to near-integrable Hamiltonians.
But as a first step toward a non-perturbative analysis,
we extend the domain of R to include any Hamiltonian
for which a certain non-resonance condition holds.