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- W4324257856 abstract "Non-smooth vector fields do not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane, non-smooth vector fields can be chaotic, a feature impossible for the smooth or continuous case. We propose a new approach to better understand chaos for non-smooth vector fields by using the notion of entropy of a system. We construct a metric space of all possible trajectories of a non-smooth vector field, where we define a flow inherited by the vector field and then define the topological entropy in this scenario. As a consequence, we are able to obtain some general results and give some examples of planar non-smooth vector fields with positive (finite and infinite) entropy." @default.
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- W4324257856 date "2023-07-01" @default.
- W4324257856 modified "2023-10-17" @default.
- W4324257856 title "On topological entropy of piecewise smooth vector fields" @default.
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- W4324257856 doi "https://doi.org/10.1016/j.jde.2023.02.053" @default.
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