Calculating box dimension with the method of types

Autor:	Kolossváry, István
Rok vydání:	2021
Předmět:	Mathematics - Metric Geometry Mathematics - Classical Analysis and ODEs Mathematics - Dynamical Systems Primary 28A80 Secondary 37C45
Druh dokumentu:	Working Paper
Popis:	This paper presents a general procedure based on using the method of types to calculate the box dimension of sets. The approach unifies and simplifies multiple box counting arguments. In particular, we use it to generalize the formula for the box dimension of self-affine carpets of Gatzouras-Lalley and of Bara\'nski type to their higher dimensional sponge analogues. In addition to a closed form, we also obtain a variational formula which resembles the Ledrappier-Young formula for Hausdorff dimension. Comment: 14 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.11049 Zobrazit plný text záznamu View this record from Arxiv