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Symmetries in symbolic dynamics

Appears in collection : Multidimensional symbolic dynamics and lattice models of quasicrystals / Dynamique symbolique multidimensionnelle et modèles de quasi-cristaux sur réseau

The automorphism group of a symbolic system captures its symmetries, reecting the dynamical behavior and the complexity of the system. It can be quite complicated: for example, for a topologically mixing shift of nite type, the automorphism group contains isomorphic copies of all nite groups and the free group on two generators and such behavior is common for shifts of high complexity. In the opposite setting of low complexity, there are numerous restrictions on the automorphism group, and for many classes of symbolic systems, it is known to be virtually abelian. I will give an overview of relations among dynamical properties of the system, algebraic properties of the automorphism group, and measurable properties of associated systems, all of which quickly lead to open questions.

Information about the video

Date of recording 02/04/2024
Date of publication 29/04/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20157503
Cite this video Kra, Bryna (02/04/2024). Symmetries in symbolic dynamics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20157503
URL https://dx.doi.org/10.24350/CIRM.V.20157503

Domain(s)

Dynamical Systems

Bibliography

HARTMAN, Yair, KRA, Bryna, et SCHMIEDING, Scott. The stabilized automorphism group of a subshift. International Mathematics Research Notices, 2022, vol. 2022, no 21, p. 17112-17186. - https://doi.org/10.1093/imrn/rnab204
SCHMIEDING, Scott. Local P entropy and stabilized automorphism groups of subshifts. Inventiones mathematicae, 2022, vol. 227, no 3, p. 963-995. - https://doi.org/10.1007/s00222-021-01076-8

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