Towards Brin’s conjecture on frame flow ergodicity:  new progress and perspectives

Cekić, Mihajlo; Lefeuvre, Thibault; Moroianu, Andrei; Semmelmann, Uwe

doi:10.5802/mrr.11

Towards Brin’s conjecture on frame flow ergodicity: new progress and perspectives

Cekić, Mihajlo ¹ ; Lefeuvre, Thibault ² ; Moroianu, Andrei ³ ; Semmelmann, Uwe ⁴

¹ Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
² Université de Paris and Sorbonne Université, CNRS, IMJ-PRG, F-75006 Paris, France
³ Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405 Orsay, France
⁴ Institut für Geometrie und Topologie, Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Mathematics Research Reports, Tome 3 (2022), pp. 21-34.

Résumé

We report on some recent progress on the ergodicity of the frame flow of negatively-curved Riemannian manifolds. We explain the new ideas leading to ergodicity for nearly $0.25$ -pinched manifolds and give perspectives for future work.

Reçu le : 2022-04-12
Révisé le : 2022-04-22
Publié le : 2022-06-30

DOI : 10.5802/mrr.11

Classification : 37A05, 37A20, 37A25, 53C10, 53C22
Mots clés : frame flow, geodesic flow, classical mechanics, ergodic theory, Pestov identity, Riemannian geometry, negative curvature, structure group, transitivity group, Parry’s free monoid, partially hyperbolic dynamical system

Affiliations des auteurs :

Cekić, Mihajlo ¹ ; Lefeuvre, Thibault ² ; Moroianu, Andrei ³ ; Semmelmann, Uwe ⁴

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Cekić, Mihajlo; Lefeuvre, Thibault; Moroianu, Andrei; Semmelmann, Uwe. Towards Brin’s conjecture on frame flow ergodicity:  new progress and perspectives. Mathematics Research Reports, Tome 3 (2022), pp. 21-34. doi : 10.5802/mrr.11. http://archive.numdam.org/articles/10.5802/mrr.11/

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