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Symmetries of nonlinear vibrations in tetrahedral molecular configurations

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  • We study nonlinear vibrational modes of oscillations for tetrahedral configurations of particles. In the case of tetraphosphorus, the interaction of atoms is given by bond stretching and van der Waals forces. Using the equivariant gradient degree, we present a topological classification of the spatio-temporal symmetries of the periodic solutions with finite Weyl's group. This procedure describes all the symmetries of the nonlinear vibrations for general force fields.

    Mathematics Subject Classification: 37J45, 34C25, 37G40, 47H11, 70H33.


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  • Figure 1.  Stationary solution to equation (2) with tetrahedral symmetries

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