Random M\"obius dynamics on the unit disc and perturbation theory for Lyapunov exponents

Florian Dorsch; Hermann Schulz-Baldes

Random M\"obius dynamics on the unit disc and perturbation theory for Lyapunov exponents

Mathematical Physics 2021-01-25 v2 math.MP

Authors: Florian Dorsch , Hermann Schulz-Baldes

Abstract

Randomly drawn $2\times 2$ matrices induce a random dynamics on the Riemann sphere via the M\"obius transformation. Considering a situation where this dynamics is restricted to the unit disc and given by a random rotation perturbed by further random terms depending on two competing small parameters, the invariant (Furstenberg) measure of the random dynamical system is determined. The results have applications to the perturbation theory of Lyapunov exponents which are of relevance for one-dimensional discrete random Schr\"odinger operators.

Keywords

random mobius dynamics unit disc lyapunov exponents furstenberg measure perturbation theory random schrodinger operators

Cite

@article{arxiv.2008.02174,
  title  = {Random M\"obius dynamics on the unit disc and perturbation theory for Lyapunov exponents},
  author = {Florian Dorsch and Hermann Schulz-Baldes},
  journal= {arXiv preprint arXiv:2008.02174},
  year   = {2021}
}

Comments

improvements throughout, new numerical results and open questions, to appear in Discrete and Continuous Dynamical Systems, Series B

Random M\"obius dynamics on the unit disc and perturbation theory for Lyapunov exponents

Abstract

Keywords

Cite

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