Periodic solutions of perturbed Hamiltonian systems in the plane by the use of the Poincaré-Birkhoff theorem
From MaRDI portal
Publication:1947829
zbMath1277.34046MaRDI QIDQ1947829
Alessandro Fonda, Fabio Zanolin, Sabatini, Marco
Publication date: 26 April 2013
Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)
Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Dynamical aspects of twist maps (37E40) Nonlinear ergodic theorems (47H25)
Related Items
Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres ⋮ Existence and stability of periodic solutions for a forced pendulum with time-dependent damping ⋮ Lower bound on the number of periodic solutions for asymptotically linear planar Hamiltonian systems ⋮ A systematic approach to nonresonance conditions for periodically forced planar Hamiltonian systems ⋮ An avoiding cones condition for the Poincaré-Birkhoff theorem ⋮ Periodic perturbations of Hamiltonian systems ⋮ Planar Hamiltonian systems at resonance: the Ahmad-Lazer-Paul condition ⋮ Periodic solutions with prescribed minimal period of vortex type problems in domains ⋮ Periodic and subharmonic solutions with winding number for \(p\)-Laplacian equations by the Poincaré-Birkhoff theorem ⋮ Positive periodic solutions to an indefinite Minkowski-curvature equation ⋮ Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments ⋮ Subharmonic solutions of weakly coupled Hamiltonian systems ⋮ Periodic solutions of Hamiltonian systems coupling twist with generalized lower/upper solutions ⋮ Bifurcations from a normally degenerate cycle in forced planar differential equations ⋮ An extension of the Poincaré-Birkhoff theorem coupling twist with lower and upper solutions ⋮ A multiplicity result for periodic solutions of second-order differential equations with a singularity ⋮ Periodic solutions to superlinear planar Hamiltonian systems ⋮ Periodic solutions of discontinuous Duffing equations ⋮ The period functions' higher order derivatives ⋮ Multiple Periodic Solutions for a Duffing Type Equation with One-Sided Sublinear Nonlinearity: Beyond the Poincaré-Birkhoff Twist Theorem ⋮ The Poincaré-Birkhoff theorem for a class of degenerate planar Hamiltonian systems ⋮ On the applicability of the Poincaré-Birkhoff twist theorem to a class of planar periodic predator-prey models ⋮ Periodic Solutions to a Perturbed Relativistic Kepler Problem ⋮ Stable and unstable periodic solutions of the forced pendulum of variable length ⋮ Periodic solutions of planar Hamiltonian systems with asymmetric nonlinearities ⋮ Many periodic solutions for a second order cubic periodic differential equation ⋮ A Poincaré-Birkhoff theorem for Hamiltonian flows on nonconvex domains ⋮ Bifurcation of relative equilibria generated by a circular vortex path in a circular domain ⋮ Unnamed Item ⋮ Periodic solutions for a dumbbell satellite equation ⋮ Global structure of subharmonics in a class of periodic predator-prey models ⋮ Periodic solutions of perturbed central Hamiltonian systems ⋮ Planar Hamiltonian systems: index theory and applications to the existence of subharmonics ⋮ Periodic and unbounded motions in asymmetric oscillators at resonance