No finite invariant density for Misiurewicz exponential maps

Janina Kotus; Grzegorz Świa̧tek

doi:10.1016/j.crma.2008.03.013

Dynamical Systems

No finite invariant density for Misiurewicz exponential maps
[Il n'existe aucune densité intégrable pour des applications exponentielles de Misiurewic]

Présenté par : Étienne Ghys

Janina Kotus ¹ ; Grzegorz Świa̧tek ^1,²

¹ Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661 Warsaw, Poland
² Department of Mathematics, Penn State University, University Park, PA 16802, USA

Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 559-562.

Résumé
Abstract

Pour les applications exponentielles de $C$ dont l'orbite de la valeur singulière 0 est bornée, on montre qu'il n'existe aucune densité intégrable et invariante sous la dynamique.

For exponential mappings such that the orbit of the only singular value 0 is bounded, it is shown that no integrable density invariant under the dynamics exists on $C$ .

Reçu le : 2007-12-20
Accepté le : 2008-03-07
Publié le : 2008-04-17

DOI : 10.1016/j.crma.2008.03.013

Affiliations des auteurs :

Janina Kotus ¹ ; Grzegorz Świa̧tek ^{1, 2}

¹ Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661 Warsaw, Poland
² Department of Mathematics, Penn State University, University Park, PA 16802, USA

@article{CRMATH_2008__346_9-10_559_0,
     author = {Janina Kotus and Grzegorz \'Swia̧tek},
     title = {No finite invariant density for {Misiurewicz} exponential maps},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {559--562},
     publisher = {Elsevier},
     volume = {346},
     number = {9-10},
     year = {2008},
     doi = {10.1016/j.crma.2008.03.013},
     language = {en},
}

TY  - JOUR
AU  - Janina Kotus
AU  - Grzegorz Świa̧tek
TI  - No finite invariant density for Misiurewicz exponential maps
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 559
EP  - 562
VL  - 346
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crma.2008.03.013
LA  - en
ID  - CRMATH_2008__346_9-10_559_0
ER  -

%0 Journal Article
%A Janina Kotus
%A Grzegorz Świa̧tek
%T No finite invariant density for Misiurewicz exponential maps
%J Comptes Rendus. Mathématique
%D 2008
%P 559-562
%V 346
%N 9-10
%I Elsevier
%R 10.1016/j.crma.2008.03.013
%G en
%F CRMATH_2008__346_9-10_559_0

Janina Kotus; Grzegorz Świa̧tek. No finite invariant density for Misiurewicz exponential maps. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 559-562. doi : 10.1016/j.crma.2008.03.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.03.013/

Bibliographie
Cité par

[1] H. Bock On the dynamics of entire functions on the Julia set, Result. Math., Volume 30 (1996), pp. 16-20

[2] N. Dobbs; B. Skorulski Non-existence of absolutely continuous invariant probabilities for exponential maps, Fund. Math., Volume 198 (2008), pp. 283-287

[3] A.È. Erëmenko; M. Lyubich Dynamical properties of some classes of entire functions, Ann. Inst. Fourier (Grenoble), Volume 42 (1992), pp. 989-1020

[4] J. Graczyk; J. Kotus; G. Świa̧tek Non-recurrent meromorphic functions, Fund. Math., Volume 182 (2004), pp. 269-281

[5] J. Kotus; M. Urbański Existence of invariant measures for transcendental subexpanding functions, Math. Z., Volume 243 (2003), pp. 25-36

[6] J. Kotus, G. Świa̧tek, Invariant measures for meromorphic Misiurewicz maps, Math. Proc. Cambr. Phil. Soc., in press

Cité par Sources :

^⁎ The first author is partially supported by a grant Chaos, fraktale i dynamika konforemna – N N201 0222 33. The second author acknowledges sabbatical support from Penn State University.

Commentaires - Politique