Expanding cocycles for interval maps

Neil Dobbs

doi:10.1016/j.crma.2007.06.002

Dynamical Systems

Expanding cocycles for interval maps

Presented by: Jean-Michel Bismut

Neil Dobbs ¹

¹ Université Paris-Sud, laboratoire de mathématiques, bâtiment 425, 91405 Orsay cedex, France

Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 39-44.

Abstract
Résumé

We give a cocycle expansivity result for $C^{2}$ multimodal interval maps with non-flat critical points. It extends the Mañé hyperbolicity theorem to also describe orbits which pass near critical points.

On étend le théorème d'hyperbolicité de Mañé pour traiter des orbites qui passent par des voisinages critiques pour des applications multimodales de l'intervalle. On démontre que, pour des cocycles bien adaptés, ces applications sont dilatantes.

Received: 2005-12-21
Accepted: 2007-06-01
Published online: 2007-07-01

DOI: 10.1016/j.crma.2007.06.002

Author's affiliations:

Neil Dobbs ¹

¹ Université Paris-Sud, laboratoire de mathématiques, bâtiment 425, 91405 Orsay cedex, France

@article{CRMATH_2007__345_1_39_0,
     author = {Neil Dobbs},
     title = {Expanding cocycles for interval maps},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {39--44},
     publisher = {Elsevier},
     volume = {345},
     number = {1},
     year = {2007},
     doi = {10.1016/j.crma.2007.06.002},
     language = {en},
}

TY  - JOUR
AU  - Neil Dobbs
TI  - Expanding cocycles for interval maps
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 39
EP  - 44
VL  - 345
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2007.06.002
LA  - en
ID  - CRMATH_2007__345_1_39_0
ER  -

%0 Journal Article
%A Neil Dobbs
%T Expanding cocycles for interval maps
%J Comptes Rendus. Mathématique
%D 2007
%P 39-44
%V 345
%N 1
%I Elsevier
%R 10.1016/j.crma.2007.06.002
%G en
%F CRMATH_2007__345_1_39_0

Neil Dobbs. Expanding cocycles for interval maps. Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 39-44. doi : 10.1016/j.crma.2007.06.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.06.002/

References
Cited by

[1] W. de Melo; S. van Strien One-Dimensional Dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Results in Mathematics and Related Areas (3), vol. 25, Springer-Verlag, Berlin, 1993

[2] J. Graczyk; D. Sands; G. Swiatek Metric attractors for smooth unimodal maps, Ann. of Math., Volume 159 (2004) no. 2

[3] R. Mañé Hyperbolicity, sinks and measure in one-dimensional dynamics, Comm. Math. Phys., Volume 100 (1985) no. 4, pp. 495-524

[4] S. van Strien; E. Vargas Real bounds, ergodicity and negative Schwarzian for multimodal maps, J. Amer. Math. Soc., Volume 17 (2004) no. 4, pp. 749-782 (electronic)

Cited by Sources:

Comments - Policy