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Resonance tongues in the quasi-periodic hill-Schrödinger equation with three frequencies

Autor
Puig, J.; Simó, C.
Tipus d'activitat
Document cientificotècnic
Data
2010-07
Codi
[prepr2010087PuiS]
Repositori
http://hdl.handle.net/2117/11094 Obrir en finestra nova
URL
http://www.ma1.upc.edu/~jpuig/preprints/puig-simo_10_2.pdf Obrir en finestra nova
Resum
In this paper we investigate numerically the following Hill’s equation x00 + (a + bq(t))x = 0 where q(t) = cos t + cosp2t + cosp3t is a quasiperiodic forcing with three rationally independent frequencies. It appears,also, as the eigenvalue equation of a Schr¨odinger operator with quasi-periodic potential. Massive numerical computations were performed for the rotation number and the Lyapunov exponent in order to detect open and collapsed gaps, resonance tongues. Our results show that the quasi...
Paraules clau
Quasi-periodic Schr\"odinger Operators, Quasi-periodic Cocycles And Skew-products, Spectral Gaps, Resonance Tongues, Rotation Number, Lyapunov Exponent, Numerical Explorations
Grup de recerca
SD - Sistemes Dinàmics de la UPC

Participants

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