Isochronicity of plane polynomial Hamiltonian systems

@article{Gavrilov1997IsochronicityOP,
  title={Isochronicity of plane polynomial Hamiltonian systems},
  author={Lubomir Gavrilov},
  journal={Nonlinearity},
  year={1997},
  volume={10},
  pages={433-448}
}
  • L. Gavrilov
  • Published 1 March 1997
  • Mathematics
  • Nonlinearity
We study isochronous centres of plane polynomial Hamiltonian systems, and more generally, isochronous Morse critical points of complex polynomial Hamiltonian functions. Our first result is that if the Hamiltonian function H is a non-degenerate semi-weighted homogeneous polynomial, then it cannot have an isochronous Morse critical point, unless the associate Hamiltonian system is linear, that is to say H is of degree two. Our second result gives a topological obstruction for isochronicity… 

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