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Résumé : To a primitive substitution system, we assign a complex matrix cocycle, defined over a toral endomorphism induced by the substitution matrix. It is closely related to the spectral theory of suspension flows over the substitution system ; in particular, the local dimension of spectral measures is expressed in terms of the top Lyapunov exponent of the cocycle. As an application, we obtain a sufficient condition for the singularity of a typical flow.
The construction and the results are also extended to S-adic system and translation flows.
Based on joint work with A. Bufetov.
Lieu : FRUMAM - Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
En savoir plus : Séminaire Teich
Résumé : TBA
Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
39 rue Frédéric Joliot-Curie
13453 MARSEILLE cedex 13
En savoir plus : Séminaire Probabilités et Statistique
Résumé : We show that the geodesic flow of any Finsler metric of constant positive flag curvature is Liouville integrable. Using this, we show that, in dimension 2, the geodesic flow is conjugate to that of the Katok metrics.
Based on joint results with R. Bryant, S. Ivanov, V. Matveev and W. Ziller.
Lieu : FRUMAM - Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
En savoir plus : Séminaire Teich
Résumé : + Punctual Participation : Pascal HUBERT/ Pierre LAZAG/ Juan MARSHALL/ Adrien BOULANGER
Titre : Spectral properties of parabolic flows
This working group will continue work on spectral properties of parabolic flows. The global objective is to give a quantitative description of the spectral measure. The first quantitative estimates for the spectral measures were obtained by the authors in a series of papers starting in 2012 through 2018. We have however only so far been able to obtain upper bounds for the spectral measure, and the aim of this workshop will be to give lower bounds as well.
Lieu : CIRM Luminy - Marseille
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