- 09-150 R. Calleja, R. de la Llave
- A numerically accessible criterion for the
breakdown of quasi-periodic solutions and its rigorous justification
Aug 31, 09
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Abstract. We formulate and justify rigorously a numerically efficient criterion
for the computation
of the analyticity breakdown of
quasi-periodic solutions in Symplectic maps (any dimension)
~and 1-D Statistical
Mechanics models. Depending on the physical interpretation of the model, the ana
breakdown may correspond to the onset of mobility of dislocations, or of spin wa
ves (in the
1-D models) and to the onset of global transport in symplectic twist maps
The criterion proposed here is based on the blow-up
of Sobolev norms of the hull functions.
We prove theorems that justify the criterion. These theorems
are based on an abstract implicit function theorem, which unifies several
results in the literature. The proofs also lead to fast
algorithms, which have been implemented and used elsewhere.
The method can be adapted to other contexts.