Open AccessON THE CLASSIFICATION OF FUNCTION GERMS OF TWO VARIABLES THAT ARE EQUIVARIANT SIMPLE WITH RESPECT TO AN ACTION OF THE CYCLIC GROUP OF ORDER THREE
Author(s) -
Е. А. Асташов
Publication year - 2016
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2016-22-3-4-7-13
Subject(s) - equivariant map , mathematics , simple (philosophy) , automorphism , action (physics) , order (exchange) , group (periodic table) , function (biology) , combinatorics , pure mathematics , germ , automorphism group , mathematical analysis , physics , biology , evolutionary biology , economics , philosophy , epistemology , finance , quantum mechanics
We consider the problem to classify function germs (C2 , 0) → (C, 0), that are equivariant simple with respect to nontrivial actions of the group Z3 on C2 and on C up to equivariant automorphism germs (C2 , 0) → (C2 , 0). The complete classification of such germs is obtained in the case of nonscalar action of Z3 on C2 that is nontrivial in both coordinates. Namely, a germ is equivariant simple with respect to such a pair of actions if and only if it is equivalent to ine of the following germs:(x, y) → x3k+1 + y2 , k ≥ 1;(x, y) → x2y + y3k−1 , k ≥ 2;(x, y) → x4 + xy3(x, y) → x4 + y5 .