We establish a Poincaré-Dulac theorem for sequences of holomorphic contractions whose differentials split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of contraction. Our results are actually stated in the framework of bundle maps.
Such sequences of holomorphic contractions appear naturally as iterated inverse branches of endomorphisms of . In this context, our normalization result allows to estimate precisely the distortions of ellipsoids along typical orbits. As an application, we show how the Lyapunov exponents of the equilibrium measure are approximated in terms of the multipliers of the repulsive cycles.
Nous démontrons un théorème de Poincaré-Dulac pour des suites de contractions holomorphes à différentielles scindées. Les relations de résonance qui déterminent les formes normales portent sur les modules des taux exponentiels de contractions. Les résultats sont formulés dans le cadre des applications fibrées.
De telles suites de contractions holomorphes apparaissent naturellement comme branches inverses d’endomorphismes de . Dans ce contexte, notre résultat de normalisation nous permet d’estimer précisément les distorsions des ellipsoides le long d’orbites typiques. Nous en déduisons que les exposants de Lyapounov de la mesure d’équilibre sont approchés par les multiplicateurs des cycles répulsifs.
Keywords: Normalization, Poincaré-Dulac theorem, Lyapounov exponents
Mot clés : Normalisation, théorème de Poincaré-Dulac, exposants de Lyapounov
@article{AIF_2008__58_6_2137_0, author = {Berteloot, Fran\c{c}ois and Dupont, Christophe and Molino, Laura}, title = {Normalization of bundle holomorphic contractions and applications to dynamics}, journal = {Annales de l'Institut Fourier}, pages = {2137--2168}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {6}, year = {2008}, doi = {10.5802/aif.2409}, zbl = {1151.37038}, mrnumber = {2473632}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2409/} }
TY - JOUR AU - Berteloot, François AU - Dupont, Christophe AU - Molino, Laura TI - Normalization of bundle holomorphic contractions and applications to dynamics JO - Annales de l'Institut Fourier PY - 2008 SP - 2137 EP - 2168 VL - 58 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2409/ DO - 10.5802/aif.2409 LA - en ID - AIF_2008__58_6_2137_0 ER -
%0 Journal Article %A Berteloot, François %A Dupont, Christophe %A Molino, Laura %T Normalization of bundle holomorphic contractions and applications to dynamics %J Annales de l'Institut Fourier %D 2008 %P 2137-2168 %V 58 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2409/ %R 10.5802/aif.2409 %G en %F AIF_2008__58_6_2137_0
Berteloot, François; Dupont, Christophe; Molino, Laura. Normalization of bundle holomorphic contractions and applications to dynamics. Annales de l'Institut Fourier, Volume 58 (2008) no. 6, pp. 2137-2168. doi : 10.5802/aif.2409. http://archive.numdam.org/articles/10.5802/aif.2409/
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