二维线性共环的边际不稳定率注记

Pub Date : 2023-01-12 DOI:10.1080/14689367.2023.2210518

I. Morris, Jonah Varney

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引用次数: 1

摘要

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。

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

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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