Recently I have much interest in algebraic topology and algebraic geometry. I am a student of the field of complex dynamical systems. According to my knowledge, my friends told me that there are many applications of algebraic geometry and algebraic topology in reduction of dimension in statistics and some other fields. I want to know whether there exist some interesting applications of algebraic geometry and algebraic topology in dynamical systems. Any comments and advice will be appreciated. Thanks.



Are there some original papers or books related to applications of algebraic topology and algebraic geometry in complex dynamic systems
The first application of algebraic geometry to dynamical systems that comes to my mind is the following preprint of Gromov -- very old one : ON THE ENTROPY OF HOLOMORPHIC MAPS


[https://www.ihes.fr/~gromov/wp-content/uploads/2018/08/1024.pdf](https://www.ihes.fr/%7Egromov/wp-content/uploads/2018/08/1024.pdf)


A recent, excellent survey of dynamics on algebraic surfaces is :


<http://perso.univ-rennes1.fr/serge.cantat/Articles/dyn-aut.pdf>


