منابع مشابه
Sturmian and Spectral Theory for Discrete Symplectic Systems
We consider 2n× 2n symplectic difference systems together with associated discrete quadratic functionals and eigenvalue problems. We establish Sturmian type comparison theorems for the numbers of focal points of conjoined bases of a pair of symplectic systems. Then, using this comparison result, we show that the numbers of focal points of two conjoined bases of one symplectic system differ by a...
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Rotation configurations for quadratic angles exhibit self-similar dynamics. Visually, it may be considered as quite evident. However, no additional details have yet been published on the exact nature of the arithmetical reasons that support this fact. In this paper, to support the existence of self-similar dynamic in 2d-configuration, we will use the constructive 1-d substitution theory in orde...
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In this study, we are concerned with introducing Weyl-Titchmarsh theory for a class of dynamic linear Hamiltonian nabla systems over a half-line on Sturmian time scales. After developing fundamental properties of solutions and regular spectral problems, we introduce the corresponding maximal and minimal operators for the system. Matrix disks are constructed and proved to be nested and converge ...
متن کاملSingular Sturmian theory for linear Hamiltonian differential systems
We establish a Sturmian type theorem comparing the number of focal points of any conjoined basis of a nonoscillatory linear Hamiltonian differential system with the number of focal points of the principal solution. We also present various extensions of this statement.
متن کاملApplications of standard Sturmian words to elementary number theory
This note is a short survey, by no means intended to be complete, of some of the descriptions which have been given of standard Sturmian words, and of some of the applications of these descriptions to elementary number theory.. (‘Elementary number theory’ is interpreted fairly broadly.) The descriptions and applications below have appeared before, expect for Fact 4, Application 1, and the proof...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 1998
ISSN: 1331-4343
DOI: 10.7153/mia-01-36