Hyperbolicity of the Trace Map for a Strongly Coupled Quasiperiodic Schrodinger Operator

2009/05/19 by Emiliano De Simone, De Simone, Emiliano, Laurent Marin +1
Mathematics · Physics and Astronomy · #37B10 #37D15 #81Q10 #82B44 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP #msc:37B10 #msc:37D15 #msc:81Q10 #msc:82B44

paper · pdf · doi:10.48550/arxiv.0905.3082

20 pages, 3 figures

arxiv created 2009/05/19 · arxiv updated 2009/12/01

Abstract

We consider the trace map associated with the silver ratio Schrodinger operator as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this map is hyperbolic if the coupling is sufficiently large. As a consequence, for this values of the coupling constant, the local and global Hausdorff dimension and the local and global box counting dimension of the spectrum of this operator all coincide and are smooth functions of the coupling constant.

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