Abstract
In this chapter, we study finite dimensional approximation methods for Hamiltonian systems. In Section 1, we study the Galerkin approximation method for Hamiltonian systems. Then in Section 2 we define the functional corresponding to the general nonlinear Hamiltonian systems on the space L of square integrable periodic functions and study its basic properties. In Section 3 we introduce the saddle point reduction method. In Section 4 we study the dimension of the kernal of the reduced functional corresponding to the given Hamiltonian system. In Section 5, we derive certain useful estimates on the reduced functional. Results in Sections 2 to 5 form the most basic part of the saddle point reduction method.
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© 2002 Springer Basel AG
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Long, Y. (2002). The variational functional. 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_4
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DOI: https://doi.org/10.1007/978-3-0348-8175-3_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9466-1
Online ISBN: 978-3-0348-8175-3
eBook Packages: Springer Book Archive