Connecting fast-slow systems and Conley index theory via transversality.
Kuehn, Christian (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Displaying similar documents to “Existence of periodic orbits for vector fields via Fuller index and the averaging method.”
Connecting fast-slow systems and Conley index theory via transversality.
One-parameter families of brake orbits in dynamical systems
Lennard Bakker (1999)
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We give a clear and systematic exposition of one-parameter families of brake orbits in dynamical systems on product vector bundles (where the fiber has the same dimension as the base manifold). A generalized definition of a brake orbit is given, and the relationship between brake orbits and periodic orbits is discussed. The brake equation, which implicitly encodes information about the brake orbits of a dynamical system, is defined. Using the brake equation, a one-parameter family of...
Harmonic solutions to perturbations of periodic separated variables ODEs on manifolds.
Spadini, Marco (2003)
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Multiplicity of forced oscillations for scalar differential equations.
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Nontrivial periodic solutions of asymptotically linear Hamiltonian systems.
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Eight-shaped Lissajous orbits in the Earth-Moon system
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Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. These equilibrium points are known as the Lagrange points (Euler points or libration points) . The existence of families of periodic and quasi-periodic orbits around these points is well known (see [, , , , ]). Among them, halo orbits are 3-dimensional periodic orbits diffeomorphic to circles. They are the first kind of the so-called Lissajous orbits. To be selfcontained,...
Remarks on bounded solutions for some nonautonomous ODE.
Dzedzej, Zdzisław (2003)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Existence of periodic solution for perturbed generalized Liénard equations.
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