SophieGermainV1, Main, Exploration, bibRecord, 000036

$${SL(2, \mathbb{R})}$$ S L ( 2 , R ) -invariant probability measures on the moduli spaces of translation surfaces are regular

Identifieur interne : 000036 ( Main/Exploration ); précédent : 000035; suivant : 000037

$${SL(2, \mathbb{R})}$$ S L ( 2 , R ) -invariant probability measures on the moduli spaces of translation surfaces are regular

Auteurs : Artur Avila [France, Brésil] ; Carlos Matheus [France] ; Jean-Christophe Yoccoz [France]

Source :

Geometric and Functional Analysis [ 1016-443X ] ; 2013-12-01.

RBID : ISTEX:FB9C7E13249C319AFF34B45AFF25FD1CA3DD281B

Abstract

Abstract: In the moduli space $${{\mathcal {H}}_g}$$ H g of normalized translation surfaces of genus g, consider, for a small parameter ρ > 0, those translation surfaces which have two non-parallel saddle-connections of length ⩽ ρ. We prove that this subset of $${{\mathcal {H}}_g}$$ H g has measure o(ρ 2) w.r.t. any probability measure on $${{\mathcal {H}}_g}$$ H g which is invariant under the natural action of $${SL(2,\mathbb{R})}$$ S L ( 2 , R ) . This implies that any such probability measure is regular, a property which is important in relation with the recent fundamental work of Eskin–Kontsevich–Zorich on the Lyapunov exponents of the KZ-cocycle.

Url:

https://api.istex.fr/document/FB9C7E13249C319AFF34B45AFF25FD1CA3DD281B/fulltext/pdf

DOI: 10.1007/s00039-013-0244-5

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Istex, to step Corpus: 000366
to stream Istex, to step Curation: 000341
to stream Istex, to step Checkpoint: 000033
to stream Main, to step Merge: 000036
to stream Main, to step Curation: 000036

Le document en format XML

<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">$${SL(2, \mathbb{R})}$$ S L ( 2 , R ) -invariant probability measures on the moduli spaces of translation surfaces are regular</title>
<author><name sortKey="Avila, Artur" sort="Avila, Artur" uniqKey="Avila A" first="Artur" last="Avila">Artur Avila</name>
</author>
<author><name sortKey="Matheus, Carlos" sort="Matheus, Carlos" uniqKey="Matheus C" first="Carlos" last="Matheus">Carlos Matheus</name>
</author>
<author><name sortKey="Yoccoz, Jean Christophe" sort="Yoccoz, Jean Christophe" uniqKey="Yoccoz J" first="Jean-Christophe" last="Yoccoz">Jean-Christophe Yoccoz</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:FB9C7E13249C319AFF34B45AFF25FD1CA3DD281B</idno>
<date when="2013" year="2013">2013</date>
<idno type="doi">10.1007/s00039-013-0244-5</idno>
<idno type="url">https://api.istex.fr/document/FB9C7E13249C319AFF34B45AFF25FD1CA3DD281B/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000366</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000366</idno>
<idno type="wicri:Area/Istex/Curation">000341</idno>
<idno type="wicri:Area/Istex/Checkpoint">000033</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000033</idno>
<idno type="wicri:doubleKey">1016-443X:2013:Avila A:sl:mathbb:r</idno>
<idno type="wicri:Area/Main/Merge">000036</idno>
<idno type="wicri:Area/Main/Curation">000036</idno>
<idno type="wicri:Area/Main/Exploration">000036</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">$${SL(2, \mathbb{R})}$$ S L ( 2 , R ) -invariant probability measures on the moduli spaces of translation surfaces are regular</title>
<author><name sortKey="Avila, Artur" sort="Avila, Artur" uniqKey="Avila A" first="Artur" last="Avila">Artur Avila</name>
<affiliation wicri:level="3"><country xml:lang="fr">France</country>
<wicri:regionArea>CNRS UMR 7586, Institut de Mathématiques de Jussieu - Paris Rive Gauche, Bâtiment SophieGermain, Case 7012, 75205, Paris Cedex 13</wicri:regionArea>
<placeName><region type="region" nuts="2">Île-de-France</region>
<settlement type="city">Paris</settlement>
</placeName>
</affiliation>
<affiliation wicri:level="3"><country xml:lang="fr">Brésil</country>
<wicri:regionArea>IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro</wicri:regionArea>
<placeName><settlement type="city">Rio de Janeiro</settlement>
<region type="state">État de Rio de Janeiro</region>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
</affiliation>
</author>
<author><name sortKey="Matheus, Carlos" sort="Matheus, Carlos" uniqKey="Matheus C" first="Carlos" last="Matheus">Carlos Matheus</name>
<affiliation wicri:level="4"><country xml:lang="fr">France</country>
<wicri:regionArea>Université Paris 13, Sorbonne Paris Cité, CNRS (UMR 7539), 93430, Villetaneuse</wicri:regionArea>
<placeName><region type="region" nuts="2">Île-de-France</region>
<settlement type="city">Villetaneuse</settlement>
</placeName>
<orgName type="university">Université Paris 13</orgName>
</affiliation>
<affiliation></affiliation>
</author>
<author><name sortKey="Yoccoz, Jean Christophe" sort="Yoccoz, Jean Christophe" uniqKey="Yoccoz J" first="Jean-Christophe" last="Yoccoz">Jean-Christophe Yoccoz</name>
<affiliation wicri:level="3"><country xml:lang="fr">France</country>
<wicri:regionArea>Collège de France (PSL), 3, Rue d’Ulm, 75005, Paris</wicri:regionArea>
<placeName><region type="region" nuts="2">Île-de-France</region>
<settlement type="city">Paris</settlement>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Geometric and Functional Analysis</title>
<title level="j" type="sub">GAFA</title>
<title level="j" type="abbrev">Geom. Funct. Anal.</title>
<idno type="ISSN">1016-443X</idno>
<idno type="eISSN">1420-8970</idno>
<imprint><publisher>Springer Basel</publisher>
<pubPlace>Basel</pubPlace>
<date type="published" when="2013-12-01">2013-12-01</date>
<biblScope unit="volume">23</biblScope>
<biblScope unit="issue">6</biblScope>
<biblScope unit="page" from="1705">1705</biblScope>
<biblScope unit="page" to="1729">1729</biblScope>
</imprint>
<idno type="ISSN">1016-443X</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">1016-443X</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: In the moduli space $${{\mathcal {H}}_g}$$ H g of normalized translation surfaces of genus g, consider, for a small parameter ρ > 0, those translation surfaces which have two non-parallel saddle-connections of length ⩽ ρ. We prove that this subset of $${{\mathcal {H}}_g}$$ H g has measure o(ρ 2) w.r.t. any probability measure on $${{\mathcal {H}}_g}$$ H g which is invariant under the natural action of $${SL(2,\mathbb{R})}$$ S L ( 2 , R ) . This implies that any such probability measure is regular, a property which is important in relation with the recent fundamental work of Eskin–Kontsevich–Zorich on the Lyapunov exponents of the KZ-cocycle.</div>
</front>
</TEI>
<affiliations><list><country><li>Brésil</li>
<li>France</li>
</country>
<region><li>État de Rio de Janeiro</li>
<li>Île-de-France</li>
</region>
<settlement><li>Paris</li>
<li>Rio de Janeiro</li>
<li>Villetaneuse</li>
</settlement>
<orgName><li>Université Paris 13</li>
</orgName>
</list>
<tree><country name="France"><region name="Île-de-France"><name sortKey="Avila, Artur" sort="Avila, Artur" uniqKey="Avila A" first="Artur" last="Avila">Artur Avila</name>
</region>
<name sortKey="Avila, Artur" sort="Avila, Artur" uniqKey="Avila A" first="Artur" last="Avila">Artur Avila</name>
<name sortKey="Matheus, Carlos" sort="Matheus, Carlos" uniqKey="Matheus C" first="Carlos" last="Matheus">Carlos Matheus</name>
<name sortKey="Yoccoz, Jean Christophe" sort="Yoccoz, Jean Christophe" uniqKey="Yoccoz J" first="Jean-Christophe" last="Yoccoz">Jean-Christophe Yoccoz</name>
<name sortKey="Yoccoz, Jean Christophe" sort="Yoccoz, Jean Christophe" uniqKey="Yoccoz J" first="Jean-Christophe" last="Yoccoz">Jean-Christophe Yoccoz</name>
</country>
<country name="Brésil"><region name="État de Rio de Janeiro"><name sortKey="Avila, Artur" sort="Avila, Artur" uniqKey="Avila A" first="Artur" last="Avila">Artur Avila</name>
</region>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/SophieGermainV1/Data/Main/Exploration

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000036 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000036 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Mathematiques
   |area=    SophieGermainV1
   |flux=    Main
   |étape=   Exploration
   |type=    RBID
   |clé=     ISTEX:FB9C7E13249C319AFF34B45AFF25FD1CA3DD281B
   |texte=   $${SL(2, \mathbb{R})}$$ S L ( 2 , R ) -invariant probability measures on the moduli spaces of translation surfaces are regular
}}

This area was generated with Dilib version V0.6.33.
Data generation: Fri Mar 8 09:40:56 2019. Site generation: Sat Nov 19 15:43:23 2022

	Serveur d'exploration Sophie Germain
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration Sophie Germain

$${SL(2, \mathbb{R})}$$ S L ( 2 , R ) -invariant probability measures on the moduli spaces of translation surfaces are regular

$${SL(2, \mathbb{R})}$$ S L ( 2 , R ) -invariant probability measures on the moduli spaces of translation surfaces are regular

Source :

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri