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SUMMARY:A uniform ergodic theorem  - Jonathan Ben Artzi (Cambridge) 
DTSTART:20130619T082000Z
DTEND:20130619T092000Z
UID:TALK45884@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:In many fields in mathematics averages of functions under the 
 action of a unitary group arise. Flows due to transport operators appearin
 g in Kinetic Theory\, such as Vlasov systems\, are a particular example du
 e to their Hamiltonian structure. It is well known that\, in general\, the
  ergodic theorem states that ``time averages converge to spatial averages'
 '. However\, typically\, this convergence is only in the strong sense\, no
 t uniform. In this talk we first review Von Neumann's proof of the (strong
 ) ergodic theorem\, and show how to obtain uniform convergence under certa
 in geometric assumptions on the flow and the underlying functional space. 
 The main ingredients of the proof are new estimates on the associated dens
 ity of states and criteria for the global rectification of vectorfields. T
 his is joint work with Clement Mouhot.
LOCATION:MR12
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