The paper considers the rotation number for a family of linear nonautonomous Hamiltonian systems and its relation with the exponential dichotomy concept. We propose numerical techniques to compute the rotation number and we employ them to infer when a given system enjoys or not an exponential dichotomy. Comparisons with QR-based techniques for exponential dichotomy will give new insights on the structure of the spectrum for the one-dimensional quasi-periodic Schrödinger operator. Experiments on the two dimensional Schrödinger equation will be presented as well.
Rotation Number and Exponential Dichotomy for Linear Hamiltonian Systems: From Theoretical to Numerical Results
ELIA, CINZIA;
2013-01-01
Abstract
The paper considers the rotation number for a family of linear nonautonomous Hamiltonian systems and its relation with the exponential dichotomy concept. We propose numerical techniques to compute the rotation number and we employ them to infer when a given system enjoys or not an exponential dichotomy. Comparisons with QR-based techniques for exponential dichotomy will give new insights on the structure of the spectrum for the one-dimensional quasi-periodic Schrödinger operator. Experiments on the two dimensional Schrödinger equation will be presented as well.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
