On the packing dimension of weighted singular matrices on fractals

Autor:	Aggarwal, Gaurav, Ghosh, Anish
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Mathematics - Dynamical Systems 11J13 11J83 37A17
Druh dokumentu:	Working Paper
Popis:	We provide the first known upper bounds for the packing dimension of weighted singular and weighted $\omega$-singular matrices. We also prove upper bounds for these sets when intersected with fractal subsets. The latter results, even in the unweighted setting, are already new for matrices. Further, even for row vectors, our results enlarge the class of fractals for which bounds are currently known. We use methods from homogeneous dynamics, in particular we provide upper bounds for the packing dimension of points on the space of unimodular lattices, whose orbits under diagonal flows $p$-escape on average. Comment: 29 pages. Comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.11658 Zobrazit plný text záznamu View this record from Arxiv