SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 94-129, January 2021.
In this paper we analyze nonlinear dynamics of the fullerene molecule. We prove, under isotypic nonresonant assumptions, the existence of global branches of periodic solutions emerging from an icosahedral equilibrium (nonlinear normal modes). We use equivariant degree theory to prove the existence of several branches of symmetric solutions for maximal orbit types which are standing and rotating waves that propagate along the molecule with icosahedral, tetrahedral, pentagonal, and triangular symmetries. Using a model that reflects the nonlinear characteristics of the fullerene, we confirm numerically the isotypic nonresonant assumptions and apply numerical Newton's continuation method to approximate some of the predicted modes.

中文翻译：

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富勒烯分子$ C_ {60} $中的全局非线性正态模

SIAM应用动力系统杂志，第20卷，第1期，第94-129页，2021
年1月。在本文中，我们分析了富勒烯分子的非线性动力学。我们证明，在同型非共振假设下，存在从二十面体平衡（非线性正态模态）出现的周期解的全局分支。我们使用等变度理论来证明最大轨道类型的对称解的多个分支的存在，这些分支是具有正二十面体，四面体，五边形和三角形对称性的沿分子传播的驻波和旋转波。使用反映富勒烯非线性特征的模型，我们在数值上确认了同型非共振假设，并应用数值牛顿连续法来近似某些预测模式。