Lipschitz contact equivalence of function germs in R^2

Autor:	Alexandre Fernandes, Vincent Grandjean, Andrei Gabrielov, Lev Birbrair
Rok vydání:	2017
Předmět:	Pure mathematics Mathematics::Algebraic Geometry Mathematics (miscellaneous) Mathematics::Complex Variables Bounded function Mathematical analysis Partition (number theory) Germ Lipschitz continuity Theoretical Computer Science Mathematics
Zdroj:	ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :81-92
ISSN:	2036-2145 0391-173X
DOI:	10.2422/2036-2145.201503_014
Popis:	In this paper we study Lipschitz contact equivalence of continuous function germs in the plane definable in a polynomially bounded o-minimal structure, such as semialgebraic and subanalytic functions. We partition the germ of the plane at the origin into zones where the function has explicit asymptotic behavior. Such a partition is called a pizza. We show that each function germ admits a minimal pizza, unique up to combinatorial equivalence. We then show that two definable continuous function germs are definably Lipschitz contact equivalent if and only if their corresponding minimal pizzas are equivalent.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::6f842c7053c384ee066ea95f67b07950 https://doi.org/10.2422/2036-2145.201503_014 Zobrazit plný text záznamu