By geometric theory of dynamical systems, I mean the kind found in [the book by Palis](https://www.springer.com/gp/book/9781461257059), or papers like [this one](https://arxiv.org/abs/1909.13149). In other words, dynamics on manifolds, but not specifically hyperbolic dynamical systems.


What are some recommended papers, survey articles, lecture notes, or books to read to explore this topic further? I really like this flavour of dynamics and would like to know what the modern research directions/questions are.


Thanks in advance!



What are the current research directions in the geometric theory of dynamical systems?
I think the book by Bonatti, Diaz and Viana: "Dynamics beyond uniform hyperbolicity' can give you a nice overview of one possible point of view. <https://link.springer.com/book/10.1007/b138174>


The book by Katok-Hasselblatt and their Handbook contains a lot of other points of view.


