A higher dimensional Poincaré-Birkhoff theorem for Hamiltonian flows
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Publication:523076
DOI10.1016/j.anihpc.2016.04.002zbMath1442.37076OpenAlexW2394939255MaRDI QIDQ523076
Alessandro Fonda, Antonio J. Ureña
Publication date: 20 April 2017
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.anihpc.2016.04.002
Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12) Symplectic and canonical mappings (37J11) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)
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Cites Work
- Unnamed Item
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- Periodic perturbations of Hamiltonian systems
- Multiplicity of solutions of variational systems involving \(\phi\)-Laplacians with singular \(\phi\) and periodic nonlinearities
- Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations
- Periodic solutions of weakly coupled superlinear systems
- The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold
- Generalizations of the Poincaré-Birkhoff theorem
- Proof of the Poincaré-Birkhoff fixed point theorem
- Forced second order conservative systems with periodic nonlinearity
- Cohomology and Morse theory for strongly indefinite functionals
- A generalized saddle point theorem
- Monotone twist maps and periodic solutions of systems of Duffing type
- Subharmonic Solutions for Some Second-Order Differential Equations with Singularities
- Periodic Solutions of Pendulum-Like Hamiltonian Systems in the Plane
- Monotone twist mappings and the calculus of variations
- Lyusternik-Schnirelman Theory for Flows and Periodic Orbits for Hamiltonian Systems on T n × R n
- A note on the Poincaré—Birkhoff fixed point theorem and periodic solutions of planar systems
- On the periodic nonlinearity and the multiplicity of solutions
- Corrigenda to: Introduction to Symplectic Topology
- Some remarks on the Poincaré-Birkhoff theorem
- On a Class of Functionals Invariant under a Z n Action
- A relative category and applications to critical point theory for strongly indefinite functionals
- A Generalization of the Poincare-Birkhoff Theorem
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