no. 9-10
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

Kotus, Janina1 ; Świa̧tek, Grzegorz1, 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, Tome 346 (2008) no. 9-10, pp. 559-562.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.03.013
Kotus, Janina 1 ; Świa̧tek, Grzegorz 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 
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Kotus, Janina; Świa̧tek, Grzegorz. No finite invariant density for Misiurewicz exponential maps. Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 559-562. doi : 10.1016/j.crma.2008.03.013. http://www.numdam.org/articles/10.1016/j.crma.2008.03.013/

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

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

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

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

[5] Kotus, J.; Urbański, M. 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.