Global Nonlinear Normal Modes in the Fullerene Molecule $C_{60}$

DOI10.1137/19M1269865zbMath1469.82043OpenAlexW3122589518MaRDI QIDQ4983523

Manuel Tejada-Wriedt, Hao-pin Wu, Wiesław Krawcewicz, Carlos García-Azpeitia

Publication date: 20 April 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1269865

zbMATH Keywords

icosahedral symmetrynonlinear normal modesequivariant degreeNewtonian systemmolecular configurations

Mathematics Subject Classification ID

Growth and boundedness of solutions to ordinary differential equations (34C11) Atomic physics (81V45) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Statistical mechanics of nanostructures and nanoparticles (82D80)

Uses Software

• GitHub
• EquiDeg

Cites Work

• A short treatise on the equivariant degree theory and its applications
• Global bifurcations of critical orbits of \(G\)-invariant strongly indefinite functionals
• The principle of symmetric criticality
• Molecular vibrational modes of \(C_{60}\) and \(C_{70}\) via finite element method
• Transformation groups
• Relative equilibria of molecules
• Applications of degree for \(S^1\)-equivariant gradient maps to variational nonlinear problems with \(S^1\)-symmetries
• Molecular chains interacting by Lennard-Jones and Coulomb forces
• Continuation of periodic orbits in conservative and Hamiltonian systems
• The symmetry perspective. From equilibrium to chaos in phase space and physical space
• Shapes and cycles arising at the steady bifurcation with icosahedral symmetry
• Symmetries of nonlinear vibrations in tetrahedral molecular configurations
• Dihedral molecular configurations interacting by Lennard-Jones and Coulomb forces
• Multiple periodic solutions for \(\Gamma\)-symmetric Newtonian systems
• Applications of equivariant degree for gradient maps to symmetric Newtonian systems
• Some global results for nonlinear eigenvalue problems
• Normal modes for nonlinear Hamiltonian systems
• Periodic solutions near equilibria of symmetric Hamiltonian systems
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein
• Classification of homotopy classes of equivariant gradient maps
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