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.
Recording during the meeting "Dynamics beyond uniform hyperbolicity" the May 16, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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Recording during the meeting "Dynamics beyond uniform hyperbolicity" the May 16, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities:
- Chapter markers and keywords to watch the parts of your choice in the video
- Videos enriched with abstracts, bibliographies, Mathematics Subject Classification
- Multi-criteria search by author, title, tags, mathematical area
Andrey Gogolev: Rigidity in rank one: dynamics and geometry - lecture 3 amulet meaning | |
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