Bounds on the Lyapunov exponent via crude estimates on the density of states

DOI10.1007/s00220-015-2324-xzbMath1358.37065arXiv1407.6433OpenAlexW3099937576MaRDI QIDQ2351061

Mira Shamis, Thomas Spencer

Publication date: 26 June 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6433

zbMATH Keywords

Schrödinger operatorChirikov (standard) map

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical aspects of twist maps (37E40)

Related Items

Dynamics and spectral theory of quasi-periodic Schrödinger-type operators ⋮ Lower bounds on the Lyapunov exponents of stochastic differential equations ⋮ Positive Lyapunov exponent for some Schrödinger cocycles over strongly expanding circle endomorphisms ⋮ Lyapunov exponents for random perturbations of some area-preserving maps including the standard map

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On stochastic sea of the standard map
• The dynamics of the Hénon map
• Random versus deterministic exponents in a rich family of diffeomorphisms
• Zur Operatorenmethode in der klassischen Mechanik
• Plenty of elliptic islands for the standard family of area preserving maps
• La théorie générale de la mesure dans son application à l'étude des systèmes dynamiques de la mécanique non linéaire
• Elliptic isles in families of area-preserving maps
• Large coupling behaviour of the Lyapunov exponent for tight binding one-dimensional random systems
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
• On the Lyapounov Exponents of Schrödinger Operators Associated with the Standard Map