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.
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