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Multiple periodic solutions to nonlinear discrete Hamiltonian systems. (English) Zbl 1152.39013

The author considers discrete Hamiltonian systems that are discrete analogs of the continuous systems of the form \( \dot x(t) =J\nabla H(x(t)), \) where \(J\) is the standard symplectic matrix, \(\nabla H\) is the gradient of a function \(H\). Using the Morse Index theory he gives several sufficient conditions for the existence of multiple \(p\)-periodic solutions to the discrete systems with \(p\) being a prime number.

MSC:

39A11 Stability of difference equations (MSC2000)
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
39A12 Discrete version of topics in analysis
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References:

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