A higher-dimensional Poincaré-Birkhoff theorem without monotone twist

DOI10.1016/j.crma.2016.01.023zbMath1382.37054OpenAlexW2306441179MaRDI QIDQ1695392

Antonio J. Ureña, Alessandro Fonda

Publication date: 7 February 2018

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2016.01.023

zbMATH Keywords

Hamiltonian systemPoincaré-Birkhoff theoremmonotone twist

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Related Items (6)

An avoiding cones condition for the Poincaré-Birkhoff theorem ⋮ Unnamed Item ⋮ Multiple Periodic Solutions for a Duffing Type Equation with One-Sided Sublinear Nonlinearity: Beyond the Poincaré-Birkhoff Twist Theorem ⋮ A new fixed point theorem and periodic solutions of nonconservative weakly coupled systems ⋮ Multiplicity of periodic solutions for systems of weakly coupled parametrized second order differential equations ⋮ Monotonicity of the period function and chaotic dynamics in a class of singular ODEs

Cites Work

• Unnamed Item
• The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold
• Cohomology and Morse theory for strongly indefinite functionals
• A relative category and applications to critical point theory for strongly indefinite functionals

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