Publication: On topological entropy of piecewise smooth vector fields
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Date
2023-07-25
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Coadvisor
Graduate program
Undergraduate course
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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.
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English
Citation
Journal of Differential Equations, v. 362, p. 52-73.
