Abstract
In this chapter, we study the relations between the index function theory on P τ(2n) and other Morse index theories for Hamiltonian or Lagrangian systems. In Section 7.1, we study the Galerkin approximation method for Hamiltonian systems. In Section 7.2, we give a simple proof for the coincidence of the Morse index of second order Hamiltonian systems with the 1-index defined in Chapter 5 of the corresponding linearized first order Hamiltonian systems. In Section 3, based on J. Duistermaat’s work [Dui1], we study the general Lagrangian systems.
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© 2002 Springer Basel AG
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Long, Y. (2002). Relations with other Morse indices. In: Index Theory for Symplectic Paths with Applications. Progress in Mathematics, vol 207. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8175-3_7
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DOI: https://doi.org/10.1007/978-3-0348-8175-3_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9466-1
Online ISBN: 978-3-0348-8175-3
eBook Packages: Springer Book Archive