Historical relation between computer science and the theory of dynamical systems
Yes there did seem to be historically a strong connection between study of dynamical systems and advanced theoretical computer science, that is shifted dramatically over time. Some of this has become mainstream and incorporated into more "core CS" (for example the empirical study of algorithms running on the SAT transition point and their strong thermodynamic/physics analogies, or empirically studied behavior of differential equations too difficult to solve exactly, etc) and some of it has moved into separate areas of more "applied" research, eg simulations of complex systems. Here are some refs on the history that might be helpful:


Chaos, the making of a new science by Gleick
Complexity, the emerging science at the edge of order and chaos by Waldrop