非可逆平面自阿芬集合

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2024-05-08 DOI:10.1017/s0305004124000136

ANTTI KÄENMÄKI, PETTERI NISSINEN

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引用次数: 0

摘要

我们比较了不可反转自证集的维度和相应的可反转自证集的维度。特别是，对于一般的平面自阿芬集合，我们证明，当它们的维数较大时，它们的维数是重合的，而当它们的维数较小时，它们的维数是不同的。我们的研究依赖于热力学形式主义，对于主矩阵和不可还原矩阵，我们可以完全描述压力的行为特征。

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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Non-invertible planar self-affine sets

We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and differ when they are small. Our study relies on thermodynamic formalism where, for dominated and irreducible matrices, we completely characterise the behaviour of the pressures.

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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.