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Ergodic Theory of the Geodesic Flow ...

Velozo, Anibal.

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Ergodic Theory of the Geodesic Flow and Entropy at Infinity.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Ergodic Theory of the Geodesic Flow and Entropy at Infinity./
Author:	Velozo, Anibal.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	158 p.
Notes:	Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Contained By:	Dissertation Abstracts International79-10B(E).
Subject:	Theoretical mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10816596
ISBN:	9780438048096

Ergodic Theory of the Geodesic Flow and Entropy at Infinity.
Velozo, Anibal.

Ergodic Theory of the Geodesic Flow and Entropy at Infinity. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 158 p.

Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.

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

In this thesis we study the geodesic flow on a non-compact pinched negatively curved manifold. We prove the upper semi-continuity of the entropy map and relate the escape of mass phenomenon with the topological entropy at infinity of the geodesic flow. We also study the thermodynamic formalism of the geodesic flow. We obtain a complete description of the pressure map of potentials that vanish at infinity, and construct Holder potentials that exhibit phase transitions. We remark that phase transitions for regular potentials is a feature that can only occur in the non-compact situation. We introduce the family of strongly positive recurrent potentials and prove some important properties of such potentials. We also obtain large deviation bounds for the geodesic flow on geometrically finite manifolds and very strongly positive recurrent potentials.

ISBN: 9780438048096Subjects--Topical Terms:

3173530
Theoretical mathematics.

Ergodic Theory of the Geodesic Flow and Entropy at Infinity.
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100 1 $a Velozo, Anibal. $3 3353210
245 1 0 $a Ergodic Theory of the Geodesic Flow and Entropy at Infinity.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 158 p.
500 $a Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
500 $a Adviser: Gang Tian.
502 $a Thesis (Ph.D.)--Princeton University, 2018.
520 $a In this thesis we study the geodesic flow on a non-compact pinched negatively curved manifold. We prove the upper semi-continuity of the entropy map and relate the escape of mass phenomenon with the topological entropy at infinity of the geodesic flow. We also study the thermodynamic formalism of the geodesic flow. We obtain a complete description of the pressure map of potentials that vanish at infinity, and construct Holder potentials that exhibit phase transitions. We remark that phase transitions for regular potentials is a feature that can only occur in the non-compact situation. We introduce the family of strongly positive recurrent potentials and prove some important properties of such potentials. We also obtain large deviation bounds for the geodesic flow on geometrically finite manifolds and very strongly positive recurrent potentials.
590 $a School code: 0181.
650 4 $a Theoretical mathematics. $3 3173530
690 $a 0642
710 2 $a Princeton University. $b Mathematics. $3 2049791
773 0 $t Dissertation Abstracts International $g 79-10B(E).
790 $a 0181
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792 $a 2018
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10816596