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Finiteness theorem for multi‐ K ‐bi‐Lipschitz equivalence of map germs
Author(s) -
Birbrair Lev,
Ferreira Costa João Carlos,
Da Silva Sena Filho Edvalter,
Mendes Rodrigo
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700243
Subject(s) - mathematics , lipschitz continuity , equivalence (formal languages) , pure mathematics , polynomial , equivalence relation , set (abstract data type) , matrix equivalence , discrete mathematics , mathematical analysis , eigenvalues and eigenvectors , physics , matrix analysis , quantum mechanics , computer science , programming language
LetP k ( n , p )be the set of all real polynomial map germs f = ( f 1 , ⋯ , f p ) : ( R n , 0 ) → ( R p , 0 )with degree off 1 , ⋯ , f pless than or equal to k ∈ N . The main result of this paper shows that the set of equivalence classes ofP k ( n , p ) , with respect to multi‐ K ‐bi‐Lipschitz equivalence, is finite.