Multi- $${\mathcal {K}}$$ -bi-Lipschitz equivalence in dimension two
São Paulo Journal of Mathematical Sciences - Trang 1-13 - 2024
Tóm tắt
In this paper, we study Multi-
$${\mathcal {K}}$$
-equivalence of multi-germs of functions on the plane, definable in a polynomially bounded o-minimal structure. As in Birbrair et al. (Annali SNS Pisa 17:81–92, 2017.
https://doi.org/10.2422/2036-2145.201503_014
), we partition the germ of the plane at origin into zones of arcs in such a way that it produces a non-Archimedean space (set of orders and width functions) compatible with a given multi-germ, encoding its asymptotic behaviour. Such a partition is called Multi-pizza. We show the existence, uniqueness and complete invariance of multi-pizzas with respect to the Multi-
$${\mathcal {K}}$$
-bi-Lipschitz equivalence.
Tài liệu tham khảo
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