For an Axiom A basic set, C-dense means that the flow is mixing; I think that
the terminology comes from the connection with the density of strong stable
(contracting) leaves.
tfisher (2017-07-03 10:23:47 -0700 -0700):
Ponce and Varao
[PonceVarao]
recently proved a rigidity result that
characterizes when an invariant measure for the time-1 map of a flow will be
invariant measure for the flow. Surprisingly, the result is very general and
does not require hyperbolic properties for the flow.
Comments
No, cf [quas2011weak]
For an Axiom A basic set, C-dense means that the flow is mixing; I think that the terminology comes from the connection with the density of strong stable (contracting) leaves.
Ponce and Varao [PonceVarao] recently proved a rigidity result that characterizes when an invariant measure for the time-1 map of a flow will be invariant measure for the flow. Surprisingly, the result is very general and does not require hyperbolic properties for the flow.