PermalinkSubmitted by rpotrie on Thu, 06/29/2017 - 12:03

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.

PermalinkSubmitted by shub on Mon, 07/10/2017 - 10:07

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.

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## John Franks and Bob Williams

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

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

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