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Geometrical Analysis of Solutions of Two Dimensional Periodic Dynamical Systems

The aim of this paper is to bring to light the properties provided to the phase plane by a generic two dimensional periodic autonomous dynamical systems (PADS) vectorfield. An associated periodic parameters linear equation (APPLE) is defined in each point of the phase plane. It is shown that the local behavior of the initial PADS trajectories is related to the value the Floquet - Liapunov exponents of this APPLE. A method to compute the Floquet - Liapunov exponent value without integration is used. So, it is possible to predict some characteristic patterns of trajectories as funneling, resonance, period doubling, sensitivity to initial conditions. Moreover, the equation of a manifold periodically crossed by the solutions is carried out. The method is applied to periodic Van der Pol and Duffing equations.
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