I am a graduate student, holding a B. Sc. from Assiut University, Egypt. My research interests are in dynamical systems. I would like to know, what are the most active research areas in the theory of dynamical systems today?
As a starting point, I suggest this computing-oriented reference (and more specifically the section §2.3.3 dedicated to ODEs/PDEs) :
H. Jaeger, "Towards a Generalized Theory Comprising Digital, Neuromorphic and Unconventional Computing", 2021 - https://iopscience.iop.org/article/10.1088/2634-4386/abf151/pdf