Problem 6

Primary tabs

Zeta function for Axiom A flows and systems

  1.  topological identification (try 1-dimensional $\Omega $ first); conjugacy invariance of $\zeta (0)$.
  2. For $C^\infty $ flows, $\zeta (s) $ has a meromorphic extension to the complex plane.

  3. Connection with Laplacian vs. geodesic results; automorphic forms.

  4. Anosov actions.



Pertaining to (b) True for analytic flows ([1]) and for  contact Anosov flows ([2])


  1. [fried1995meromorphic] Fried D.  1995.  Meromorphic zeta functions for analytic flows. Communications in mathematical physics. 174:161–190.
  2. [giulietti2012anosov] Giulietti P, Liverani C, Pollicott M.  2012.  Anosov flows and dynamical zeta functions. arXiv preprint arXiv:1203.0904.

Add a new comment

Log in or register to post comments