Linear Hamiltonian Systems: Quadratic Integrals, Singular Subspaces and Stability

  title={Linear Hamiltonian Systems: Quadratic Integrals, Singular Subspaces and Stability},
  author={Valery V. Kozlov},
  journal={Regular and Chaotic Dynamics},
  • V. V. Kozlov
  • Published 5 February 2018
  • Mathematics
  • Regular and Chaotic Dynamics
A chain of quadratic first integrals of general linear Hamiltonian systems that have not been represented in canonical form is found. Their involutiveness is established and the problem of their functional independence is studied. The key role in the study of a Hamiltonian system is played by an integral cone which is obtained by setting known quadratic first integrals equal to zero. A singular invariant isotropic subspace is shown to pass through each point of the integral cone, and its… 

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