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On Effective Equidistribution of Erg...

Kim, Minsung.

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On Effective Equidistribution of Ergodic Averages for Higher Step Nilflows and Higher Rank Actions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	On Effective Equidistribution of Ergodic Averages for Higher Step Nilflows and Higher Rank Actions./
Author:	Kim, Minsung.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	212 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-09, Section: B.
Contained By:	Dissertations Abstracts International82-09B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27670576
ISBN:	9798582510772

On Effective Equidistribution of Ergodic Averages for Higher Step Nilflows and Higher Rank Actions.
Kim, Minsung.

On Effective Equidistribution of Ergodic Averages for Higher Step Nilflows and Higher Rank Actions. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 212 p.

Source: Dissertations Abstracts International, Volume: 82-09, Section: B.

Thesis (Ph.D.)--University of Maryland, College Park, 2020.

This item must not be sold to any third party vendors.

In the first part of the thesis, we prove the bounds of ergodic averages for nilflows on general higher step nilmanifolds. It is well known that a flow is not renormalizable on higher step nilpotent Lie algebras and it is not possible to adapt the methods of analysis in moduli space. Instead, we develop the technique called 'scaling method' for operators behaves like renormalization. On the space of Lie algebra satisfying the "transverse" condition, we obtain the speed of convergence of ergodic averages with the polynomial type of exponent regarding the structure of nilpotent Lie algebras.In the second part, we introduce the results on higher rank actions on Heisenberg nilmanifolds. We develop the method for higher rank action by following the work of A.Bufetov and G.Forni. We construct the finitely-additive measure called Bufetov functional and obtain the prove deviation of ergodic averages on Heisenberg nilmanifolds. As an application, we prove the limit theorem of normalized ergodic integrals.

ISBN: 9798582510772Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Deviation of ergodic averages

On Effective Equidistribution of Ergodic Averages for Higher Step Nilflows and Higher Rank Actions.
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100 1 $a Kim, Minsung. $3 1905007
245 1 0 $a On Effective Equidistribution of Ergodic Averages for Higher Step Nilflows and Higher Rank Actions.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 212 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-09, Section: B.
500 $a Advisor: Forni, Giovanni.
502 $a Thesis (Ph.D.)--University of Maryland, College Park, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a In the first part of the thesis, we prove the bounds of ergodic averages for nilflows on general higher step nilmanifolds. It is well known that a flow is not renormalizable on higher step nilpotent Lie algebras and it is not possible to adapt the methods of analysis in moduli space. Instead, we develop the technique called 'scaling method' for operators behaves like renormalization. On the space of Lie algebra satisfying the "transverse" condition, we obtain the speed of convergence of ergodic averages with the polynomial type of exponent regarding the structure of nilpotent Lie algebras.In the second part, we introduce the results on higher rank actions on Heisenberg nilmanifolds. We develop the method for higher rank action by following the work of A.Bufetov and G.Forni. We construct the finitely-additive measure called Bufetov functional and obtain the prove deviation of ergodic averages on Heisenberg nilmanifolds. As an application, we prove the limit theorem of normalized ergodic integrals.
590 $a School code: 0117.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Deviation of ergodic averages
653 $a Dynamical systems
653 $a Ergodic theory
653 $a Higher rank actions
653 $a Nilflows
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a University of Maryland, College Park. $b Mathematics. $3 1266601
773 0 $t Dissertations Abstracts International $g 82-09B.
790 $a 0117
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27670576