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Regul. Chaotic Dyn., 2018, Volume 23, Issue 6, Pages 638–653 (Mi rcd356)  

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

Ernest Fontich, Carles Simó, Arturo Vieiro

Departament de Matemàtiques i Informàtica, Universitat de Barcelona, BGSMath, Gran Via 585, 08007, Barcelona, Catalonia

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

Funding Agency Grant Number
Ministerio de Economía y Competitividad de España MTM2016-80117-P
Ministry of Science and Innovation of Spanish MDM2014-0445
Agència de Gestiö d'Ajuts Universitaris i de Recerca 2017-SGR-1374
This work has been supported by grants MTM2016-80117-P, MDM2014-0445 (Spain) and 2017-SGR-1374 (Catalonia).


DOI: https://doi.org/10.1134/S1560354718060011

References: PDF file   HTML file

Bibliographic databases:

MSC: 37C55, 37J40, 37J45
Received: 10.07.2018
Accepted:04.09.2018
Language:

Citation: Ernest Fontich, Carles Simó, Arturo Vieiro, “On the “Hidden” Harmonics Associated to Best Approximants Due to Quasi-periodicity in Splitting Phenomena”, Regul. Chaotic Dyn., 23:6 (2018), 638–653

Citation in format AMSBIB
\Bibitem{FonSimVie18}
\by Ernest Fontich, Carles Sim\'o, Arturo Vieiro
\paper On the “Hidden” Harmonics Associated to Best Approximants Due to Quasi-periodicity in Splitting Phenomena
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 6
\pages 638--653
\mathnet{http://mi.mathnet.ru/rcd356}
\crossref{https://doi.org/10.1134/S1560354718060011}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85058929329}


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