Finiteness theorem for multi‐     K   ‐bi‐Lipschitz equivalence of map germs | Zendy

Birbrair Lev | Zendy; Ferreira Costa João Carlos | Zendy; Da Silva Sena Filho Edvalter | Zendy; Mendes Rodrigo | Zendy

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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.

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