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- Title
Sharp ½-Hölder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrödinger cocycles.
- Authors
Figueras, Jordi-Lluís; Timoudas, Thomas Ohlson
- Abstract
We consider the setting for the disappearance of uniform hyperbolicity as in Bjerklöv and Saprykina (2008 Nonlinearity21), where it was proved that the minimum distance between invariant stable and unstable bundles has a linear power law dependence on parameters. In this scenario we prove that the Lyapunov exponent is sharp ½-Hölder continuous.In particular, we show that the Lyapunov exponent of Schrödinger cocycles with a potential having a unique non-degenerate minimum is sharp ½-Hölder continuous below the lowest energy of the spectrum, in the large coupling regime.
- Subjects
LYAPUNOV exponents; COCYCLES; EXPONENTS; LINEAR dependence (Mathematics); CONTINUITY; SCHRODINGER operator
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2020, Vol 40, Issue 7, p4519
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2020189