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Ergodic Theory of the Geodesic Flow ...

ProQuest Information and Learning Co.

Ergodic Theory of the Geodesic Flow and Entropy at Infinity.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Ergodic Theory of the Geodesic Flow and Entropy at Infinity./
作者:	Velozo, Anibal.
面頁冊數:	1 online resource (158 pages)
附註:	Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Contained By:	Dissertation Abstracts International79-10B(E).
標題:	Theoretical mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9780438048096

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

Ergodic Theory of the Geodesic Flow and Entropy at Infinity. - 1 online resource (158 pages)

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

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

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780438048096Subjects--Topical Terms:

1180455
Theoretical mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Ergodic Theory of the Geodesic Flow and Entropy at Infinity.
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035 $a AAI10816596
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100 1 $a Velozo, Anibal. $3 1194285
245 1 0 $a Ergodic Theory of the Geodesic Flow and Entropy at Infinity.
264 0 $c 2018
300 $a 1 online resource (158 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
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.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Theoretical mathematics. $3 1180455
655 7 $a Electronic books. $2 local $3 554714
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Princeton University. $b Mathematics. $3 1180706
773 0 $t Dissertation Abstracts International $g 79-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10816596 $z click for full text (PQDT)

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