English
Nilpotent endomorphisms of expansive group actions
Virtualconference
Auteurs : Salo, Ville (Auteur de la Conférence)
CIRM (Editeur )
37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.)
37B15 - Cellular automata
54H15 - Transformation groups and semigroups, See also {20M20, 22-XX, 57Sxx}
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2313/Slides/Salo.pdf
CIRM (Editeur )
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Résumé :
We say a pointed dynamical system is asymptotically nilpotent if every point tends to zero. We study group actions whose endomorphism actions are nilrigid, meaning that for all asymptotically nilpotent endomorphisms the convergence to zero is uniform. We show that this happens for a large class of expansive group actions on a large class of groups. The main examples are cellular automata on subshifts of finite type.
Keywords : group action; expansivity; nilpotency; cellular automata
Codes MSC : Keywords : group action; expansivity; nilpotency; cellular automata
37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.)
37B15 - Cellular automata
54H15 - Transformation groups and semigroups, See also {20M20, 22-XX, 57Sxx}
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2313/Slides/Salo.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 26/01/2021 Date de captation : 12/01/2021 Sous collection : Research talks arXiv category : Dynamical Systems ; Group Theory Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 00:53:22 Audience : Researchers Download : https://videos.cirm-math.fr/2021-01-12_Sallo.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Algebraic and Combinatorial Invariants of Subshifts and Tilings / Invariants combinatoires et algébriques des décalages et des pavagesOrganisateurs de la rencontre : Berthé, Valérie ; Cortez, Maria-Isabel ; Durand, Fabien ; Hosseini, Maryam ; Petite, Samuel Dates : 11/01/2021 - 15/01/2021 Année de la rencontre : 2021 URL Congrès : https://conferences.cirm-math.fr/2313.html
Données de citation
DOI : 10.24350/CIRM.V.19697703Citer cette vidéo: Salo, Ville (2021). Nilpotent endomorphisms of expansive group actions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19697703 URI : http://dx.doi.org/10.24350/CIRM.V.19697703 |
Voir aussi
- [Multi angle] Interview au Cirm : Fabien Durand & Samuel Petite / Personne interviewée Durand, Fabien ; Personne interviewée Petite, Samuel.
- [Multi angle] Confined subgroups and high transitivity / Auteur de la Conférence Matte Bon, Nicolás.
- [Virtualconference] Rotated odometers / Auteur de la Conférence Lukina, Olga.
- [Virtualconference] Number of ergodic and generic measures for minimal subshifts / Auteur de la Conférence Fickenscher, Jon.
- [Virtualconference] Recent developments in finite rank systems / Auteur de la Conférence Donoso, Sebastián.
Bibliographie
- SALO, Ville et TÖRMÄ, Ilkka. Nilpotent Endomorphisms of Expansive Group Actions. arXiv preprint arXiv:1804.07630, 2018. - https://arxiv.org/abs/1804.07630
- TÖRMÄ, Ilkka. A uniquely ergodic cellular automaton. Journal of Computer and System Sciences, 2015, vol. 81, no 2, p. 415-442. - https://dl.acm.org/doi/abs/10.1016/j.jcss.2014.10.001
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- CULIK II, Karel, PACHL, Jan, et YU, Sheng. On the limit sets of cellular automata. SIAM Journal on Computing, 1989, vol. 18, no 4, p. 831-842. - https://doi.org/10.1137/0218057
- KARI, Jarkko. The nilpotency problem of one-dimensional cellular automata. siam Journal on Computing, 1992, vol. 21, no 3, p. 571-586. - https://doi.org/10.1137/0221036
- JALONEN, Joonatan et KARI, Jarkko. Conjugacy of one-dimensional one-sided cellular automata is undecidable. In : International Conference on Current Trends in Theory and Practice of Informatics. Edizioni della Normale, Cham, 2018. p. 227-238. - https://doi.org/10.1007/978-3-319-73117-9_16
- GUILLON, Pierre et RICHARD, Gaétan. Nilpotency and limit sets of cellular automata. In : International Symposium on Mathematical Foundations of Computer Science. Springer, Berlin, Heidelberg, 2008. p. 375-386. - https://doi.org/10.1007/978-3-540-85238-4_30
- SALO, Ville. On nilpotency and asymptotic nilpotency of cellular automata. arXiv preprint arXiv:1205.6714, 2012. - https://www.villesalo.com/article/ONaANoCA.pdf
