A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian flows

  • Alessandro Fonda

    Dipartimento di Matematica e Geoscienze, Università di Trieste, P. le Europa 1, I-34127 Trieste, Italy
  • Antonio J. Ureña

    Departamento de Matemática Aplicada, Universidad de Granada, Facultad de Ciencias, 18071 Granada, Spain

Abstract

We propose an extension to higher dimensions of the Poincaré–Birkhoff Theorem which applies to Poincaré time-maps of Hamiltonian systems. Examples of applications to pendulum-type systems and weakly-coupled superlinear systems are also given.

Cite this article

Alessandro Fonda, Antonio J. Ureña, A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 679–698

DOI 10.1016/J.ANIHPC.2016.04.002