由一维动力学引起的巴拿赫空间仿射等距的一些例子

IF 0.9 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2025-07-31 DOI:10.1016/j.exmath.2025.125716

Andrés Navas

引用次数: 0

摘要

我们提供了大量的Banach空间C0(S1), L1（S1）和L2（S1×S1）的仿射等距的例子，尽管它们是循环的（特别是，它们具有零漂移），但它们是不定点的。这些来自于圆微分同态群上的自然环，即对数、仿射和（Schwarzian导数的一种变化）。非常有趣的是，它们起源于在适当的上下文中具有普遍性的微分同构。我们还展示了如何推广这些例子，以获得满足相同性质的交换等距族。

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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Some examples of affine isometries of Banach spaces arising from 1-D dynamics

We provide a large family of examples of affine isometries of the Banach spaces

C^{0} (S^{1})

L^{1} (S^{1})

and

L^{2} (S^{1} \times S^{1})

that are fixed-point-free despite being recurrent (in particular, they have zero drift). These come from natural cocycles on the group of circle diffeomorphisms, namely the logarithmic, affine and (a variation of the) Schwarzian derivative. Quite interestingly, they arise from diffeomorphisms that are generic in an appropriate context. We also show how to promote these examples in order to obtain families of commuting isometries satisfying the same properties.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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