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

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.