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Multi angle

Authors : Gogolev, Andrey (Author of the conference)
CIRM (Publisher )

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Abstract : A dynamical system is called rigid if a weak form of equivalence with a nearby system, such as coincidence of some simple invariants, implies a strong form of equivalence. In this minicourse we will discuss smooth rigidity of hyperbolic dynamical systems and related geometric questions such as marked length spectrum rigidity of negatively curved manifolds. We will consider the following moduli: lengths of periodic orbits, spectra of Poincar\'e return maps of the periodic orbits, volume Lyapunov exponents. After a brief overview of some classical results we will focus on recent developments in rigidity of Anosov and partially hyperbolic systems as well as connections to geometric rigidity. The latter is based on joint work with B. Kalinin and V. Sadovskaya and with F. Rodriguez Hertz.

Keywords : Anosov diffeomorphisms; Anosov flows; partially hyperbolic; marked length spectrum rigidity; rigidity

MSC Codes :
37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)

Additional resources :
https://www.cirm-math.fr/RepOrga/1947/Notes/Gogolyev-Rigidity-notes2.pdf

Information on the Video

Film maker :

Recanzone, Luca

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Download :

https://videos.cirm-math.fr/2019-05-14_Cogolev_Part2.mp4

Information on the Event

Event Title : Dynamique au-delà de l'hyperbolicité uniforme / Dynamics Beyond Uniform Hyperbolicity
Event Organizers : Bonatti, Christian ; Buzzi, Jérôme ; Crovisier, Sylvain ; Gan, Shaobo ; Pacifico, Maria José
Dates : 13/05/2019 - 24/05/2019
Event Year : 2019
Event URL : https://conferences.cirm-math.fr/1947.html

Citation Data

DOI : 10.24350/CIRM.V.19526503
Cite this video as: Gogolev, Andrey (2019). Rigidity in rank one: dynamics and geometry - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19526503
URI : http://dx.doi.org/10.24350/CIRM.V.19526503

See Also

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