Each finite group is a symmetry group of some map (an ``Atom''-bifurcation)
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 21-29
Voir la notice de l'article provenant de la source Math-Net.Ru
Maps are studied, i.e. cell decompositions of closed two-dimensional surfaces, or two-dimensional atoms, which encode bifurcations of Liouville fibrations of nondegenerate integrable Hamiltonian systems. Any finite group $G$ is proved to be the symmetry group of an orientable map (of an atom). Moreover one such a map $X(G)$ is constructed algorithmically. Upper bounds are obtained for the minimal genus M$g(G)$ of an orientable map with the given symmetry group $G,$ and for the minimal number of vertices, edges and sides of such maps.
@article{VMUMM_2013_3_a2,
author = {E. A. Kudryavtseva and A. T. Fomenko},
title = {Each finite group is a symmetry group of some map (an {``Atom''-bifurcation)}},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {21--29},
publisher = {mathdoc},
number = {3},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a2/}
}
TY - JOUR AU - E. A. Kudryavtseva AU - A. T. Fomenko TI - Each finite group is a symmetry group of some map (an ``Atom''-bifurcation) JO - Vestnik Moskovskogo universiteta. Matematika, mehanika PY - 2013 SP - 21 EP - 29 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a2/ LA - ru ID - VMUMM_2013_3_a2 ER -
%0 Journal Article %A E. A. Kudryavtseva %A A. T. Fomenko %T Each finite group is a symmetry group of some map (an ``Atom''-bifurcation) %J Vestnik Moskovskogo universiteta. Matematika, mehanika %D 2013 %P 21-29 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a2/ %G ru %F VMUMM_2013_3_a2
E. A. Kudryavtseva; A. T. Fomenko. Each finite group is a symmetry group of some map (an ``Atom''-bifurcation). Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 21-29. http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a2/