Coupling linearity and twist: an extension of the Poincaré-Birkhoff theorem for Hamiltonian systems

DOI10.1007/s00030-020-00653-9zbMath1454.37057OpenAlexW3092337553MaRDI QIDQ2211041

Alessandro Fonda, Paolo Gidoni

Publication date: 10 November 2020

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-020-00653-9

zbMATH Keywords

periodic solutionsHamiltonian systemsPoincaré-Birkhoff theorem

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Related Items (7)

An extension of the Poincaré-Birkhoff theorem for Hamiltonian systems coupling resonant linear components with twisting components ⋮ Periodic solutions of weakly coupled superlinear systems with indefinite terms ⋮ Periodic solutions of Hamiltonian systems coupling twist with generalized lower/upper solutions ⋮ An extension of the Poincaré-Birkhoff theorem coupling twist with lower and upper solutions ⋮ Multiplicity results for Hamiltonian systems with Neumann-type boundary conditions ⋮ Multiplicity of clines for systems of indefinite differential equations arising from a multilocus population genetics model ⋮ Existence of a periodic solution for superlinear second order ODEs

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