A note on the marginal instability rates of two-dimensional linear cocycles

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2023-01-12 DOI:10.1080/14689367.2023.2210518

I. Morris, Jonah Varney

引用次数: 1

Abstract

A theorem of Guglielmi and Zennaro implies that if the uniform norm growth of a locally constant -cocycle on the full shift is not exponential, then it must be either bounded or linear, with no other possibilities occurring. We give an alternative proof of this result and demonstrate that its conclusions do not hold for Lipschitz continuous cocycles over the full shift on two symbols.

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二维线性共环的边际不稳定率注记

Guglielmi和Zennaro的一个定理表明，如果一个局部常数环在全位移上的一致范数增长不是指数增长，那么它要么是有界的，要么是线性的，不存在其他可能性。我们给出了这一结果的另一种证明，并证明了它的结论对于两个符号上的全位移上的Lipschitz连续环不成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences