Problem 21

Primary tabs

Assume $\varphi _t $ $C$-dense. If $\nu $ is $\varphi _1 $ invariant is $\nu $ $\varphi $-invariant?


No, cf [1]


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 [1] 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.


Add a new comment

Log in or register to post comments