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This paper is based mainly on the joint paper with W. Kryszewski [Dzedzej, Z., Kryszewski, W.: Conley type index applied to Hamiltonian inclusions. J. Math. Anal. Appl. 347 (2008), 96–112.], where cohomological Conley type index for multivalued flows has been applied to prove the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian inclusions. Some proofs and additional remarks concerning definition of the index and special cases are given.
We generalize to higher dimension results of Birkhoff and Mather on the existence of
orbits wandering in regions of instability of twist maps. This generalization is strongly
inspired by the one proposed by Mather. However, its advantage is that it contains most
of the results of Birkhoff and Mather on twist maps.
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