The following article aims at presenting classical aspects of dynamical systems preserving a geometric structure, focusing on -dimensional Lorentzian dynamics. The reader won’t find here any new result, but rather an expository approach of classical ones. Our main goal, in particular, is to introduce part of the techniques and arguments used in [7] to obtain the classification of closed -dimensional Lorentzian manifolds admitting a non-compact isometry group. Doing so, we will present a self-contained, and somehow shortened proof of Zeghib’s classification [24] of non-equicontinuous Lorentzian isometric flows in dimension .
@article{TSG_2016-2017__34__1_0, author = {Charles Frances}, title = {Lorentzian $3$-manifolds and dynamical systems}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {1--32}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {34}, year = {2016-2017}, doi = {10.5802/tsg.353}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.353/} }
TY - JOUR AU - Charles Frances TI - Lorentzian $3$-manifolds and dynamical systems JO - Séminaire de théorie spectrale et géométrie PY - 2016-2017 SP - 1 EP - 32 VL - 34 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.353/ DO - 10.5802/tsg.353 LA - en ID - TSG_2016-2017__34__1_0 ER -
%0 Journal Article %A Charles Frances %T Lorentzian $3$-manifolds and dynamical systems %J Séminaire de théorie spectrale et géométrie %D 2016-2017 %P 1-32 %V 34 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.353/ %R 10.5802/tsg.353 %G en %F TSG_2016-2017__34__1_0
Charles Frances. Lorentzian $3$-manifolds and dynamical systems. Séminaire de théorie spectrale et géométrie, Volume 34 (2016-2017), pp. 1-32. doi : 10.5802/tsg.353. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.353/
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