Problem 31

Primary tabs

Anosov diffeos


  1. Hypothesis on $H_1(M)$
  2. Fixed points
  3. $\Omega = M$


John Franks and Bob Williams found an Anosov flow  on a manifiold $M$ whose chain recorrent set is not all of $M$.

Under some pinching assumptions on the spectrum there are some answers. See Brin, M.Manning, A.
Anosov diffeomorphisms with pinched spectrum. Dynamical systems and turbulence, Warwick 1980 (Coventry, 1979/1980), pp. 48–53, 
Lecture Notes in Math., 898, Springer, Berlin-New York, 1981.

See PORTEOUS, Hugh L. Anosov diffeomorphisms of flat manifolds. Topology, 1972, vol. 11, no 3, p. 307-315 for examples of manifolds admitting Anosov diffeomorphisms with first Betti number zero.


Add a new comment

Log in or register to post comments