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Regular and Chaotic Dynamics

, Volume 23, Issue 6, pp 638–653 | Cite as

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

  • Ernest FontichEmail author
  • Carles Simó
  • Arturo Vieiro
Article

Abstract

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.

Keywords

quasi-periodic splitting dominant harmonics hidden harmonics irrational numbers properties 

MSC

37C55 37J40 37J45 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Departament de Matemàtiques i InformàticaUniversitat de Barcelona, BGSMathBarcelona, CataloniaSpain

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