東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

On Effective Equidistribution of Erg...

Kim, Minsung.

FindBook

Google Book

Amazon

博客來

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	On Effective Equidistribution of Ergodic Averages for Higher Step Nilflows and Higher Rank Actions./
作者:	Kim, Minsung.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	212 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-09, Section: B.
Contained By:	Dissertations Abstracts International82-09B.
標題:	Mathematics. -
電子資源:	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.
LDR:02219nmm a2200373 4500 001 2280372
005 20210827095934.5
008 220723s2020 ||||||||||||||||| ||eng d
020 $a 9798582510772
035 $a (MiAaPQ)AAI27670576
035 $a AAI27670576
040 $a MiAaPQ $c MiAaPQ
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