Periodic orbits and invariant cones in three-dimensional piecewise linear systems
Victoriano Carmona Emilio Freire Soledad Fernández-García
Discrete & Continuous Dynamical Systems - A 2015, 35(1): 59-72 doi: 10.3934/dcds.2015.35.59
We deal with the existence of invariant cones in a family of three-dimensional non-observable piecewise linear systems with two zones of linearity. We find a subfamily of systems with one invariant cone foliated by periodic orbits. After that, we perturb the system by making it observable and non-homogeneous. Then, the periodic orbits that remain after the perturbation are analyzed.
keywords: Piecewise linear systems invariant manifolds invariant cones. periodic orbits half-Poincaré maps

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