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Dynamics of Kleinian groups.

Pan, Wenyu.

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Dynamics of Kleinian groups.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamics of Kleinian groups./
Author:	Pan, Wenyu.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	166 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-02, Section: B.
Contained By:	Dissertations Abstracts International80-02B.
Subject:	Theoretical Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10927863
ISBN:	9780438194335

Dynamics of Kleinian groups.
Pan, Wenyu.

Dynamics of Kleinian groups. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 166 p.

Source: Dissertations Abstracts International, Volume: 80-02, Section: B.

Thesis (Ph.D.)--Yale University, 2018.

This item must not be added to any third party search indexes.

We study several dynamical properties of flows on infinite volume homogeneous spaces and its applications. Let G be a connected simple linear Lie group of real rank one, &Ggr; be an abelian co-cover of a Zariski dense convex cocompact discrete subgroup of G, and A be a one-parameter diagonalizable subgroup of G. We start with outlining the problems we are interested in. In chapter 2, we establish that the action of A on &Ggr;\\G satisfies the local mixing property, a property we introduce to substitute the strong mixing property in infinite volume setting. In chapter 3, we classify the Radon measures on &Ggr;\\G invariant under the action of horospherical subgroups. In chapter 4, we present the classification for joining measures for horocycle flows in the case where G = PSL2([special characters omitted]) and &Ggr; is a [special characters omitted] or [special characters omitted]2-co-cover of a cocompact lattice in G. We discuss the circle counting problem in chapter 5: let P be a general circle packing in the complex plane [special characters omitted] invariant under a geometrically finite Kleinian group P. When &Ggr; is convex cocompact or its critical exponent is greater than 1, we obtain an effective equidistribution for small circles in &Ggr; intersecting any bounded connected regular set in [special characters omitted]; this provides an effective refinement to an earlier work of Oh-Shah [OS12].

ISBN: 9780438194335Subjects--Topical Terms:

1672766
Theoretical Mathematics.

Dynamics of Kleinian groups.
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245 1 0 $a Dynamics of Kleinian groups.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 166 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-02, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
502 $a Thesis (Ph.D.)--Yale University, 2018.
506 $a This item must not be added to any third party search indexes.
506 $a This item must not be sold to any third party vendors.
520 $a We study several dynamical properties of flows on infinite volume homogeneous spaces and its applications. Let G be a connected simple linear Lie group of real rank one, &Ggr; be an abelian co-cover of a Zariski dense convex cocompact discrete subgroup of G, and A be a one-parameter diagonalizable subgroup of G. We start with outlining the problems we are interested in. In chapter 2, we establish that the action of A on &Ggr;\\G satisfies the local mixing property, a property we introduce to substitute the strong mixing property in infinite volume setting. In chapter 3, we classify the Radon measures on &Ggr;\\G invariant under the action of horospherical subgroups. In chapter 4, we present the classification for joining measures for horocycle flows in the case where G = PSL2([special characters omitted]) and &Ggr; is a [special characters omitted] or [special characters omitted]2-co-cover of a cocompact lattice in G. We discuss the circle counting problem in chapter 5: let P be a general circle packing in the complex plane [special characters omitted] invariant under a geometrically finite Kleinian group P. When &Ggr; is convex cocompact or its critical exponent is greater than 1, we obtain an effective equidistribution for small circles in &Ggr; intersecting any bounded connected regular set in [special characters omitted]; this provides an effective refinement to an earlier work of Oh-Shah [OS12].
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