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Propriétés topologiques des ensembles accessibles en temps exact

Abstract : The exact time accessibilité sets, i.e. the sets of points that can be reached in a given time have some topological properties that are interesting to study. Resides the control theory, these sets are the support of transition probabilities from diffusion processes. The main result of this work is to prove that for an important class of systems (including analytical systems) the interior of the closure of these sets is the interior, and that the interior is dense in the closurs. The families of vectors field are complete. Counter-example are given showing the necessity of the hypothesis. This show that the result of Kunita are false. This work settle what can be expected
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Submitted on : Tuesday, April 24, 2018 - 3:41:07 PM
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Donatien Tondele. Propriétés topologiques des ensembles accessibles en temps exact. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1987. Français. ⟨NNT : 1987METZ012S⟩. ⟨tel-01775726⟩



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