Hausdorff dimension and infinitesimal similitudes on complete metric spaces
Dynamical Systems
2021-01-20 v1 Metric Geometry
Spectral Theory
Abstract
In this paper, we answer a question of Nussbaum, Priyadarshi, and Lunel [Positive operators and Hausdorff dimension of invariant sets, Trans. Amer. Math. Soc. 364(2) (2012) 1029-1066.]. We also show that the Hausdorff dimension and box dimension of the attractor generated by a finite set of contractive infinitesimal similitudes are the same. Further, we extend many results of dimension theory to complete metric spaces. In the last part, we fill the gaps in the proofs of some articles, which are related to the dimension theory, and hint at some possible improvements in the recent papers.
Keywords
Cite
@article{arxiv.2101.07520,
title = {Hausdorff dimension and infinitesimal similitudes on complete metric spaces},
author = {S. Verma},
journal= {arXiv preprint arXiv:2101.07520},
year = {2021}
}
Comments
20 pages