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Identifier 000402749
Title Ποσοτικά θεωρήματα επαναφοράς
Alternative Title Quantative recurrence theorems
Author Λουτράρης, Αντώνιος
Thesis advisor Κωστάκης, Γεώργιος
Reviewer Καμβύσης, Σπύρος
Φραντζικινάκης, Νίκος
Abstract In this master thesis, we present a quantitative extension of Poincare's reccurence theorem, due to Michael Boshernitzan. More precisely, given a measure preserving system (X, Φ,μ,ά,Τ) and assume that for some α > 0 the α-dimensional Hausdorff measure is σ-finite at X, then for almost x £ X, 1 In the first chapter we review some basic facts concerning Haus¬dorff measure and dimension of a set in a metric space. In the second chapter we present Birkhoff's ergodic theorem and some of its applications. In the third chapter, we formulate and prove Poincare's recurrence theorem. Finally the fourth chapter occu¬pies the proof and some applications of the above quantitative result, due to Boshernitzan.
Language Greek
Issue date 2012-07-11
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics--Post-graduate theses
 
Permanent Link https://elocus.lib.uoc.gr//dlib/0/f/1/metadata-dlib-1473835040-983063-2516.tkl Bookmark and Share
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