Branching of periodic orbits in Hamiltonian and reversible systems

Vanderbauwhede, André

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Existence of periodic solutions and homoclinic orbits for third-order nonlinear differential equations.

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Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity

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Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics...

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