A Constructive Proof of the Poincare-Birkhoff Theorem

DOI10.2307/2154925zbMath0869.54044OpenAlexW4237230762MaRDI QIDQ4846064

Yong Li, Zhenghua Lin

Publication date: 1 September 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2154925

zbMATH Keywords

constructive proofPoincaré-Birkhoff theoremperiodic solutions of Duffing equations

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (13)

A NEW CONTINUATION METHOD FOR THE PERIODICITY PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS ⋮ Constructive proof of the existence of periodic solutions to the Duffing equation ⋮ Some extensions of the Poincaré-Birkhoff theorem ⋮ Unnamed Item ⋮ A boundary perturbation interior point homotopy method for solving fixed point problems ⋮ A noninterior path following algorithm for solving a class of multiobjective programming problems ⋮ On reversible maps and symmetric periodic points ⋮ Solving fixed-point problems with inequality and equality constraints via a non-interior point homotopy path-following method ⋮ A parameter perturbation homotopy continuation method for solving fixed point problems with both inequality and equality constraints ⋮ Modified homotopy methods to solve fixed points of self-mapping in a broader class of nonconvex sets ⋮ Existence of an interior path leading to the solution point of a class of fixed point problems ⋮ Some inequality techniques in handling fixed point problems on unbounded sets via homotopy methods ⋮ Solving nonlinear programming problems with unbounded non-convex constraint sets via a globally convergent algorithm

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