Schrödinger operators with potentials generated by hyperbolic transformations. I: Positivity of the Lyapunov exponent
DOI10.1007/s00222-022-01157-2OpenAlexW3108601450WikidataQ115608880 ScholiaQ115608880MaRDI QIDQ2689276
Artur Avila, Zhenghe Zhang, David Damanik
Publication date: 9 March 2023
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2011.10146
subshift of finite typeHölder continuous functionLyapunov exponentdiscrete one-dimensional Schrödinger operators
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Discrete version of topics in analysis (39A12) Difference operators (39A70) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Symbolic dynamics (37B10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)
Related Items (5)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Livšic theorem for matrix cocycles
- Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
- Positive Lyapunov exponents and localization bounds for strongly mixing potentials
- Extremal Lyapunov exponents: an invariance principle and applications
- Spectral properties of disordered systems in the one-body approximation
- Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices. (Genericity of non-zero Lyapunov exponents for deterministic products of matrices)
- Power-law bounds on transfer matrices and quantum dynamics in one dimension
- Dynamical localization for the random dimer Schrödinger operator
- Measurable rigidity of the cohomological equation for linear cocycles over hyperbolic systems
- Continuity of Lyapunov exponents in the \(C^0\) topology
- Continuity of Lyapunov exponents for cocycles with invariant holonomies
- Conformally natural extension of homeomorphisms of the circle
- Delocalization in random polymer models
- Positive Lyapunov exponents for a class of deterministic potentials
- Uniform hyperbolicity and its relation with spectral analysis of 1D discrete Schrödinger operators
- Positive Lyapunov exponent for some Schrödinger cocycles over strongly expanding circle endomorphisms
- Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension
- A note on Lyapunov exponents of deterministic strongly mixing potentials
- Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
- Scaling diagram for the localization length at a band edge
- Almost everywhere positivity of the Lyapunov exponent for the doubling map
- Some open sets of nonuniformly hyperbolic cocycles
- Schrödinger operators with dynamically defined potentials
- On Dynamical Systems With the Specification Property
- Local product structure for Equilibrium States
- One-Dimensional Ergodic Schrödinger Operators
- Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent
- Lyapunov exponents with multiplicity 1 for deterministic products of matrices
- Noncommuting Random Products
- Periodic Points and Measures for Axiom a Diffeomorphisms
- Weak mixing directions in non-arithmetic Veech surfaces
- Some Large Deviation Results for Dynamical Systems
- Equilibrium states and the ergodic theory of Anosov diffeomorphisms
- On nonperturbative localization with quasi-periodic potential.
- Anderson localization for Schrödinger operators on \(\mathbb{Z}\) with strongly mixing potentials.
- Anderson localization for Schrödinger operators on \(\mathbb Z\) with potentials given by the skew-shift
This page was built for publication: Schrödinger operators with potentials generated by hyperbolic transformations. I: Positivity of the Lyapunov exponent
