编码为有限型子移元素的量子图的Lyapunov指数

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-08-29 DOI:10.1007/s13324-025-01122-1

Oleg Safronov

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引用次数: 0

摘要

我们考虑量子图上的Schrödinger算子，其边连接的点 \({{\mathbb {Z}}}\)．连接两个连续点n和的边的个数 \(n+1\) 是沿着有限型移位的轨道读取的。我们证明了李雅普诺夫指数对于能量E是正的，当能量E不属于 \([0,\infty )\)．这个子集中点E的个数 \([(\pi (j-1))^2, (\pi j)^2]\) 对所有人都一样吗 \(j\in {{\mathbb {N}}}\)．

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Lyapunov exponent for quantum graphs coded as elements of a subshift of finite type

We consider the Schrödinger operator on the quantum graph whose edges connect the points of \({{\mathbb {Z}}}\). The numbers of the edges connecting two consecutive points n and \(n+1\) are read along the orbits of a shift of finite type. We prove that the Lyapunov exponent is potitive for energies E that do not belong to a discrete subset of \([0,\infty )\). The number of points E of this subset in \([(\pi (j-1))^2, (\pi j)^2]\) is the same for all \(j\in {{\mathbb {N}}}\).

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.