Problem 21

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

Comments

  • Ledrappier (2016-11-14 11:47:01 -0800 -0800):
  • BrianMarcus (2016-11-14 11:47:18 -0800 -0800):

    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.