I am currently doing a historical study on my school project 'study of ODE' which slowly shift to the study of dynamical system as I am interested in pursuing my study of ode from linear system, phase portrait to dynamical system.
I had made my own study and research about the development of dynamical systems. Based on my research, the study of dynamical system started with DE. DE started since Newton and Leibniz introduced the DEs system. Then in 19th century, most of the techniques for solving elementary level of differential equations had been identified. Then till 20th century, with the works of Poincare in between 1880 - 1886, dynamical system started. My questions are :
When is the idea of equilibrium point discussed? As the study linear system phase portrait, we often started with simplex autonomous linear system which has equilibrium point at origin.
When do we have a general theory of ODE?
When do we see the study of local behaviour for a general ODE, for example 2-D linear system.
Who is the one that discover the phase portrait of linear autonomous system.
When do dynamical system view of ODE became popular?
I had found few of the contributors to dynamical system which are Henri Poincare, Stephen Smale, George David Birkhoff, Ivar Otto Bendixson and etc? Can someone help me to classify them based on their contribution according to the year?