Much more than in Riemannian geometry, isometries and conformal transformations of pseudo-Riemannian manifolds can have rich dynamics. There are, accordingly, more interesting groups acting, more complicated orbit structures, and more flexible global geometries. I will survey a few topics in dynamics on pseudo-Riemannian manifolds and present some contributions of me and my collaborators.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/8825