Recurrence for semi-decompositions
Abstract
This paper constructs a foundation to analyze semi-group actions, group actions, filtrations, and decompositions in a unified manner. In fact, though the studies of decomposition can be applied to foliated spaces and group actions, they can not be applied to semi-group actions and filtrations in general because filtration and the set of orbits of a semi-group need not be decompositions of the base spaces. To analyze these concepts in a unified manner, we introduce a concept of a semi-decomposition which is a natural generalization of these concepts because similar relations among recurrence and their variants to group actions and decompositions hold for semi-decompositions. On the other hand, we demonstrate the difference between the recurrent concepts for group actions and those even for semi-group actions.
Cite
@article{arxiv.2202.10568,
title = {Recurrence for semi-decompositions},
author = {Tomoo Yokoyama},
journal= {arXiv preprint arXiv:2202.10568},
year = {2023}
}