Sweeping by a tame process
Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 2201-2223.

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.

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.

Received:
Revised:
Accepted:
Published online:
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)
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Daniilidis, Aris; Drusvyatskiy, Dmitriy. Sweeping by a tame process. Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 2201-2223. doi : 10.5802/aif.3133. http://www.numdam.org/articles/10.5802/aif.3133/

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