Sweeping by a tame process  [ Processus de rafle modéré ]
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.

Reçu le : 2015-09-13
Révisé le : 2016-09-28
Accepté le : 2016-10-26
Publié le : 2017-11-16
DOI : https://doi.org/10.5802/aif.3133
Classification : 34A26,  34A60,  49J53,  14P10
Mots clés : Processus de rafle, semi-algébrique, o-minimal, désingularisation, sous-gradient.
@article{AIF_2017__67_5_2201_0,
     author = {Daniilidis, Aris and Drusvyatskiy, Dmitriy},
     title = {Sweeping by a tame process},
     journal = {Annales de l'Institut Fourier},
     pages = {2201--2223},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {67},
     number = {5},
     year = {2017},
     doi = {10.5802/aif.3133},
     language = {en},
     url = {archive.numdam.org/item/AIF_2017__67_5_2201_0/}
}
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. http://archive.numdam.org/item/AIF_2017__67_5_2201_0/

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