Generalized Bounded Distortion Property
Gregory Borissov, Grigorii Monakov
TL;DR
This paper establishes a nonstationary bounded distortion property for smooth dynamical systems, which could be useful for analyzing spectral properties of Schrödinger operators with Sturmian potentials.
Contribution
It introduces a nonstationary bounded distortion property for $C^{1 + \varepsilon}$ smooth systems, extending previous bounded distortion results to a nonstationary setting.
Findings
Proves the nonstationary bounded distortion property for multidimensional systems
Potential applications to spectral analysis of Schrödinger operators with Sturmian potentials
Provides a new tool for studying dynamical systems with non-uniform distortion
Abstract
We prove the Nonstationary Bounded Distortion Property for smooth dynamical systems on multidimensional spaces. The results we obtain are motivated by potential application to study of spectral properties of discrete Schr\"odinger operators with potentials generated by Sturmian sequences.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical Analysis and Transform Methods