Monotone twist maps and periodic solutions of systems of Duffing type
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Publication:2927885
DOI10.1017/S0305004114000310zbMath1331.34070MaRDI QIDQ2927885
Alberto Boscaggin, Rafael Ortega
Publication date: 4 November 2014
Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)
Periodic solutions to ordinary differential equations (34C25) Dynamical aspects of twist maps (37E40) Multifrequency systems of ordinary differential equations (34C46)
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An extension of the Poincaré-Birkhoff theorem for Hamiltonian systems coupling resonant linear components with twisting components ⋮ Periodic perturbations of Hamiltonian systems ⋮ Some remarks on the periodic motions of a bouncing ball ⋮ Periodic solutions of weakly coupled superlinear systems ⋮ A new fixed point theorem and periodic solutions of nonconservative weakly coupled systems ⋮ A higher dimensional Poincaré-Birkhoff theorem for Hamiltonian flows ⋮ Multiple periodic solutions of Hamiltonian systems confined in a box ⋮ A Poincaré-Birkhoff theorem for Hamiltonian flows on nonconvex domains ⋮ Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth ⋮ Existence of a periodic solution for superlinear second order ODEs ⋮ Unbounded solutions to systems of differential equations at resonance
Cites Work
- Unnamed Item
- The existence of quasiperiodic solutions for coupled Duffing-type equations
- Periodic solutions of Duffing's equations with superquadratic potential
- Existence of forced oscillations for some nonlinear differential equations
- Twist Mappings with Non-Periodic Angles
- Long-time stability estimates for the non-periodic Littlewood boundedness problem
- Solutions of prescribed number of zeroes to a class of superlinear ODE's systems
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