On the Lyapounov Exponents of Schrödinger Operators Associated with the Standard Map

DOI10.1007/978-1-4614-6406-8_3zbMath1273.37025arXiv1202.6399OpenAlexW1784227015MaRDI QIDQ4928663

Jean Bourgain

Publication date: 17 June 2013

Published in: Asymptotic Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.6399

zbMATH Keywords

Lyapounov exponentsstandard map

Mathematics Subject Classification ID

Quantum chaos (81Q50) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Lattice dynamics; integrable lattice equations (37K60)

Related Items (2)

Lyapunov exponents for random perturbations of some area-preserving maps including the standard map ⋮ Bounds on the Lyapunov exponent via crude estimates on the density of states

Cites Work

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• The absolutely continuous spectrum of Jacobi matrices
• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
• Plenty of elliptic islands for the standard family of area preserving maps
• Generalized Floquet theory for stationary Schrödinger operators in one dimension
• JACOBI MATRICES WITH RANDOM POTENTIALS TAKING FINITELY MANY VALUES

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