On the “Hidden” Harmonics Associated to Best Approximants Due to Quasi-periodicity in Splitting Phenomena

Resumo

The effects of quasi-periodicity on the splitting of invariant manifolds are examined. We have found that some harmonics that could be expected to be dominant in some ranges of the perturbation parameter actually are nondominant. It is proved that, under reasonable conditions, this is due to the arithmetic properties of the frequencies.