Markov partitions for non-transitive expansive flows

Ioannis Iakovoglou

doi:10.5802/crmath.682

Article de recherche - Systèmes dynamiques

Markov partitions for non-transitive expansive flows
[Partitions de Markov pour les flux expansifs non-transitifs]

Ioannis Iakovoglou ¹

¹ Université Sorbonne Paris Nord, UMR 7539 du CNRS, 99 avenue J. B. Clément, 93430 Villetaneuse, France

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 437-444.

Abstract (VO)
Résumé

In this note we construct Markov partitions for non-transitive expansive flows in dimension 3.

Dans cette note, nous construisons des partitions de Markov pour les flux expansifs non-transitifs en dimension 3.

Reçu le : 2024-07-24
Révisé le : 2024-08-29
Accepté le : 2024-08-29
Publié le : 2025-05-26

DOI : 10.5802/crmath.682

Affiliations des auteurs :

Ioannis Iakovoglou ¹

¹ Université Sorbonne Paris Nord, UMR 7539 du CNRS, 99 avenue J. B. Clément, 93430 Villetaneuse, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2025__363_G5_437_0,
     author = {Ioannis Iakovoglou},
     title = {Markov partitions for non-transitive expansive flows},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {437--444},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.682},
     language = {en},
}

TY  - JOUR
AU  - Ioannis Iakovoglou
TI  - Markov partitions for non-transitive expansive flows
JO  - Comptes Rendus. Mathématique
PY  - 2025
SP  - 437
EP  - 444
VL  - 363
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.682
LA  - en
ID  - CRMATH_2025__363_G5_437_0
ER  -

%0 Journal Article
%A Ioannis Iakovoglou
%T Markov partitions for non-transitive expansive flows
%J Comptes Rendus. Mathématique
%D 2025
%P 437-444
%V 363
%I Académie des sciences, Paris
%R 10.5802/crmath.682
%G en
%F CRMATH_2025__363_G5_437_0

Ioannis Iakovoglou. Markov partitions for non-transitive expansive flows. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 437-444. doi : 10.5802/crmath.682. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.682/

Bibliographie
Cité par

[1] Marco Brunella Expansive flows on three-manifolds, Ph. D. Thesis, International School for Advanced Studies (1992)

[2] David Fried Transitive Anosov flows and pseudo-Anosov maps, Topology, Volume 22 (1983) no. 3, pp. 299-303 | DOI | MR | Zbl

[3] Ioannis Iakovoglou A new combinatorial invariant caracterizing Anosov flows on 3-manifolds (2022) | arXiv | DOI

[4] Ioannis Iakovoglou Markovian families for Anosov-like actions (In preparation)

[5] Takashi Inaba; Shigenori Matsumoto Nonsingular expansive flows on $3$ -manifolds and foliations with circle prong singularities, Jpn. J. Math., New Ser., Volume 16 (1990) no. 2, pp. 329-340 | DOI | MR | Zbl

[6] Harvey B. Keynes; Michael Sears Real-expansive flows and topological dimension, Ergodic Theory Dyn. Syst., Volume 1 (1981) no. 2, pp. 179-195 | DOI | MR | Zbl

[7] Masatoshi Oka Singular foliations on cross-sections of expansive flows on $3$ -manifolds, Osaka J. Math., Volume 27 (1990) no. 4, pp. 863-883 | MR | Zbl

[8] Marina Ratner Markov partitions for C-flows on 3-dimensional manifolds, Mat. Zametki, Volume 6 (1969) no. 6, pp. 693-704

[9] Stephen J. Smale Differentiable dynamical systems, Bull. Am. Math. Soc., Volume 73 (1967), pp. 747-817 | DOI | MR

[10] Hassler Whitney Regular families of curves, Ann. Math. (2), Volume 34 (1933) no. 2, pp. 244-270 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique