A note on integrable two-degrees-of-freedom Hamiltonian systems with a second integral quartic in the momenta

@inproceedings{Romeiras1995ANO,
  title={A note on integrable two-degrees-of-freedom Hamiltonian systems with a second integral quartic in the momenta},
  author={Filipe J. Romeiras},
  year={1995}
}
Two of the simplest integrable Hamiltonians H(x,y,px,py,)=(px2+py2)/2+V(x,y) with a second integral quartic in the momenta are those with potentials V3(x,y)=by(3x2+16y2)+d(x2+16y2)+ eta y and V4(x,y)=a(x4+6x2y2+8y4)+c(x2+4y2)+vy-2. We show how V3 can be obtained from V4. In the process we obtain a new potential of the class, VN, that includes both V3 and V4 as particular cases. For this potential we give the second integral of motion, separating variables, a Lax representation and a bi… CONTINUE READING

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