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Published April 20, 1998 | public
Journal Article

Modified Prüfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum

Abstract

We provide a new proof of the theorem of Simon and Zhu that in the region |E|<λ for a.e. energies, −(d^2/dx^2)+λ cos(x^α), 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 with V(j^2)=e^j,V(n)=0 if n∉ {1, 4, 9,…}. The arguments depend on a direct analysis of the equations for the norm of a solution.

Additional Information

© 1998 Academic Press. Received 13 June 1997, Accepted 20 August 1997. 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.

Additional details

Created:
August 19, 2023
Modified:
October 17, 2023