no. 5
Sweeping by a tame process
[Processus de rafle modéré]
Daniilidis, Aris1 ; Drusvyatskiy, Dmitriy2
1 DIM–CMM, UMI CNRS 2807 Beauchef 851 (Torre Norte, piso 5), Universidad de Chile (Chile)
2 University of Washington Department of Mathematics C-138 Padelford, Seattle, WA 98195 (USA)
Annales de l'Institut Fourier, Tome 67 (2017) no. 5, pp. 2201-2223.

Nous montrons l’existence des solutions (orbites) absolument continues par morceaux pour le processus de rafle défini par un opérateur multivoque semi-algébrique (ou plus généralement, o-minimal). Nous établissons que de telles orbites bornées sont de longueur finie. Cette contribution, dans le cas particulier où le processus de rafle correspond aux sous-niveaux d’une fonction (non nécessairement régulière), généralise les résultats connus pour les orbites des systèmes dynamiques de type sous-gradient.

We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions (trajectories), and any such bounded trajectory must have finite length. Analogous results hold more generally for sweeping processes definable in o-minimal structures. This extends previous work on (sub)gradient dynamical systems beyond monotone sweeping sets.

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Révisé le :
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DOI : 10.5802/aif.3133
Classification : 34A26, 34A60, 49J53, 14P10
Keywords: Sweeping process, semialgebraic, o-minimal, desingularization, subgradient
Mot clés : Processus de rafle, semi-algébrique, o-minimal, désingularisation, sous-gradient.

Daniilidis, Aris 1 ; Drusvyatskiy, Dmitriy 2

1 DIM–CMM, UMI CNRS 2807 Beauchef 851 (Torre Norte, piso 5), Universidad de Chile (Chile)
2 University of Washington Department of Mathematics C-138 Padelford, Seattle, WA 98195 (USA)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Daniilidis, Aris; Drusvyatskiy, Dmitriy. Sweeping by a tame process. Annales de l'Institut Fourier, Tome 67 (2017) no. 5, pp. 2201-2223. doi : 10.5802/aif.3133. https://aif.centre-mersenne.org/articles/10.5802/aif.3133/

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