Periodic Solutions of Asymptotically Linear Autonomous Hamiltonian Systems with Resonance

In this paper we define the index at infinity of an asymptotically linear autonomous Hamiltonian system. We use this index to prove the existence and bifurcation from infinity of periodic solutions of the system. We apply the degree for G-invariant strongly indefinite functionals defined by Go??biewska and Rybicki in (Nonlinear Anal 74:1823–1834, 2011).