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

Author
Puig, J.; Simó, C.
Type of activity
Journal article
Journal
Regular and chaotic dynamics
Date of publication
2011
Volume
16
Number
1-2
First page
62
Last page
79
DOI
https://doi.org/10.1134/S1560354710520047 Open in new window
Repository
http://hdl.handle.net/2117/11329 Open in new window
URL
http://www.springerlink.com/content/02x2483t5427287u/ Open in new window
Abstract
n this article we investigate numerically the spectrum of some representative examples of discrete one-dimensional Schrödinger operators with quasi-periodic potential in terms of a perturbative constant b and the spectral parameter a. Our examples include the well-known Almost Mathieu model, other trigonometric potentials with a single quasi-periodic frequency and generalisations with two and three frequencies. We computed numerically the rotation number and the Lyapunov exponent to detect open...
Citation
Puig, J.; Simó, C. Resonance tongues in the quasi-periodic Hill-Schrödinger equation with three frequencies. "Journal of regular and chaotic dynamics", 2011, vol. 16, núm. 1-2, p. 62-79.
Group of research
SD - UPC Dynamical Systems

Participants