Abstract
We provide a new proof of the theorem of Simon and Zhu that in the region E<λfor a.e. energies, -(d2/dx2)+λcos(xα), 0<α<1 has Lyapunov behavior with a quasi-classical formula for the Lyapunov exponent. We also prove Lyapunov behavior for a.e.E∈[-2,2] for the discrete model withV(j2)=ej,V(n)=0 ifn∉{1,4,9,...}. The arguments depend on a direct analysis of the equations for the norm of a solution.
Original language | English |
---|---|
Pages (from-to) | 513-530 |
Number of pages | 18 |
Journal | Journal of Functional Analysis |
Volume | 154 |
Issue number | 2 |
DOIs | |
State | Published - 20 Apr 1998 |
Externally published | Yes |
Bibliographical note
Funding Information:* This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The U.S. Government has certain rights in this material.