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Subgroup structure of bifurcation equations with crystallographic group symmetry
Author(s) -
Makeev Oleg,
Loginov Boris
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700973
Subject(s) - bifurcation , symmetry group , symmetry (geometry) , mathematics , bifurcation theory , homogeneous space , lattice (music) , crystallographic point group , group (periodic table) , hopf bifurcation , mathematical physics , pure mathematics , crystal structure , physics , crystallography , geometry , chemistry , quantum mechanics , nonlinear system , acoustics
For stationary and Andronov‐Hopf bifurcation with symmetry of highest crystalline classes of basic syngonies of symmorphic crystallographic groups as semidirect products of translations on basic directions and point symmetry of lattice the subgroup structure of relevant bifurcation equations and bifurcating solutions dual to subgroup structure of such symmetry is investigated. Applications to phase transitions in physics are considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)