Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Vlandos Alexandros
Supervisors info:
Απόστολος Γιαννόπουλος,Καθηγητής,Τομέας Μαθηματικής ανάλυσης,ΕΚΠΑ
Αριστείδης Κατάβολος,Ομότιμος Καθηγητής,Τομέας Μαθηματικής ανάλυσης,ΕΚΠΑ
Βασιλική Φαρμάκη,Καθηγήτρια,Τομέας Μαθηματικής Ανάλυσης,ΕΚΠΑ
Original Title:
Εργοδική θεωρία δράσεων τοπικά συμπαγών ομάδων
Translated title:
Ergodic theory of actions of locally compact groups
Summary:
We study the ergodic theory of actions of locally compact groups on metric
spaces. We introduce the notion of an invariant, under such an action,
measure on the metric space, the notions of ergodicity and mixing for such
actions, and provide examples of actions which are mixing but not mixing
of higher orders. Next, we introduce the notion of amenability for locally
compact groups and show
that for every continuous action of a locally compact amenable group on a
compact metric space, via homeomorphisms, there exists a probability
measure which is invariant under the action of the group. This result
generalizes the theorem of Krylov and Bogoliouboff for actions of Z or N
and provides a characterization of amenability. We prove the mean ergodic
theorem and pointwise ergodic theorems for amenable groups. Finally, we
establish the ergodic decomposition of an invariant under a group action
probability measure.
Main subject category:
Science
Keywords:
Key Words: Ergodic theory, group actions, ergodicity, mixing. invariant measure, amenability, maximal and mean ergodic theorem, ergodic decomposition
