We prove the existence and the uniqueness of the SRB measure for any singular hyperbolic attractor in dimension . The proof does not use Poincaré sectional maps, but uses basic properties of thermodynamical formalism.
Nous prouvons que tout attracteur partiellement hyperbolique de dimension finie et avec singularité(s) admet une unique mesure SRB. La preuve utilise des outils simples et généraux du formalisme thermodynamique et ne nécessite pas de recourir à une section de Poincaré.
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Keywords: partially hyperbolic singular flows, thermodynamical formalism, equilibrium states, SRB and physical measures
Mot clés : flots partiellement hyperboliques, formalisme thermodynamique, état d’équilibre, mesures SRB et physiques
Leplaideur, Renaud 1; Yang, Dawei 2
@article{AIF_2017__67_6_2703_0, author = {Leplaideur, Renaud and Yang, Dawei}, title = {SRB measures for higher dimensional singular partially hyperbolic attractors}, journal = {Annales de l'Institut Fourier}, pages = {2703--2717}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {67}, number = {6}, year = {2017}, doi = {10.5802/aif.3148}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3148/} }
TY - JOUR AU - Leplaideur, Renaud AU - Yang, Dawei TI - SRB measures for higher dimensional singular partially hyperbolic attractors JO - Annales de l'Institut Fourier PY - 2017 SP - 2703 EP - 2717 VL - 67 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3148/ DO - 10.5802/aif.3148 LA - en ID - AIF_2017__67_6_2703_0 ER -
%0 Journal Article %A Leplaideur, Renaud %A Yang, Dawei %T SRB measures for higher dimensional singular partially hyperbolic attractors %J Annales de l'Institut Fourier %D 2017 %P 2703-2717 %V 67 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3148/ %R 10.5802/aif.3148 %G en %F AIF_2017__67_6_2703_0
Leplaideur, Renaud; Yang, Dawei. SRB measures for higher dimensional singular partially hyperbolic attractors. Annales de l'Institut Fourier, Volume 67 (2017) no. 6, pp. 2703-2717. doi : 10.5802/aif.3148. https://aif.centre-mersenne.org/articles/10.5802/aif.3148/
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