An Index Theorem for Non‐Periodic Solutions of Hamiltonian Systems

@article{Piccione1999AnIT,
  title={An Index Theorem for Non‐Periodic Solutions of Hamiltonian Systems},
  author={Paolo Piccione and Daniel V. Tausk},
  journal={Proceedings of the London Mathematical Society},
  year={1999},
  volume={83}
}
  • P. Piccione, D. Tausk
  • Published 8 November 1999
  • Mathematics
  • Proceedings of the London Mathematical Society
We consider a Hamiltonian setup M, ω, H, L, Γ, P, where M, ω is a symplectic manifold, L is a distribution of Lagrangian subspaces in M, P is a Lagrangian submanifold of M, H is a smooth time‐dependent Hamiltonian function on M, and Γ:[a,b] → M is an integral curve of the Hamiltonian flow H→ starting at P. We do not require any convexity property of the Hamiltonian function H. Under the assumption that Γ(b) is not P‐focal, we introduce the Maslov index imaslovΓ of Γ given in terms of the first… 
Lagrangian and Hamiltonian formalism for constrained variational problems
  • P. Piccione, D. Tausk
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2002
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