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arXiv · 1806.03601

Strongly Independent Matrices and Applications on the Rigidity of $A$-Invariant Measures on $n$-Torus

Huichi Huang·Enhui Shi·Hui Xu
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Abstract

We introduce the notion of strongly independent matrices and show the existence of strongly independent matrices in $GL(n,\mathbb{Z})$ over $\mathbb{Z}^n\setminus\{0\}$ when $2n+1$ is a prime number. As an application of strong independence, we give a measure rigidity result for endomorphisms on $n$-torus $\mathbb{T}^n$.

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Huichi Huang, Enhui Shi, Hui Xu. 2018-06-10. Strongly Independent Matrices and Applications on the Rigidity of $A$-Invariant Measures on $n$-Torus. https://arxiv.org/abs/1806.03601

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