The loss of stability of symmetrical equilibrium positions |
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Institution: | Pushchino, Moscow Region, Russia;Lomonosov Moscow State University, 1 Leninskiye Gory, Main Building, 119991 Moscow, Russia;Department of Quantum Field Theory, Tomsk State University, Russia |
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Abstract: | Systems of differential equations possessing a finite (or compact) symmetry group and depending on one parameter are considered. The nature of the loss of stability of equilibrium positions is investigated in cases when, owing to symmetry, the linearized problem has multiple eigenvalues. Conditions are presented that determine whether the loss of stability when the parameter is varied is soft or hard, for double eigenvalues λ - zero or pure imaginary. Cases of triple zero eigenvalues λ corresponding to tetrahedral (or cubic) symmetry, are considered. |
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