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CATEGORIES:Conference on Mathematical Topics in Kinetic Theor
y
SUMMARY:A uniform ergodic theorem - Jonathan Ben Artzi (C
ambridge)
DTSTART;TZID=Europe/London:20130619T092000
DTEND;TZID=Europe/London:20130619T102000
UID:TALK45884AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/45884
DESCRIPTION:In many fields in mathematics averages of function
s under the action of a unitary group arise. Flows
due to transport operators appearing in Kinetic T
heory\, such as Vlasov systems\, are a particular
example due to their Hamiltonian structure. It is
well known that\, in general\, the ergodic theorem
states that ``time averages converge to spatial a
verages''. However\, typically\, this convergence
is only in the strong sense\, not uniform. In this
talk we first review Von Neumann's proof of the (
strong) ergodic theorem\, and show how to obtain u
niform convergence under certain geometric assumpt
ions on the flow and the underlying functional spa
ce. The main ingredients of the proof are new esti
mates on the associated density of states and crit
eria for the global rectification of vectorfields.
This is joint work with Clement Mouhot.
LOCATION:MR12
CONTACT:HoD Secretary\, DPMMS
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