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Dynamics of a circular cylinder interacting with point vortices
Reversible Hamiltonian Liapunov center theorem
1. | IBILCE, UNESP, São José do Rio Preto, CEP 15054-000, Brazil |
2. | Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom |
In case $R$ acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point.
In case $R$ acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.
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