| Contents |
| We study the dynamics originated by the superposition of two autonomous
systems in the plane for which the origin is a local center and a saddle, respectively.
We will show that if we alternatively switch the two systems maintaining
each one for a sufficiently large time, then the overall Poincar\'e map
induces chaotic dynamics on two symbols near the origin.
In particular, under the $T$-periodicity of the switching (for $T \,$ large),
there is existence of $T$-periodic solutions and subharmonics of any
order. We will briefly provide an outline of the proof and an insight into the
main topological tool used for its fulfillment, the so called ``stretching
along the paths'' method. If time permits, we will show other configurations
(different from the center-saddle one) giving possibly rise to chaotic dynamics in the coin-tossing sense. |
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