of various sub-areas within nonlinear dynamics such as ergodicity [@Cit:ergodicity], chaos theory [@Cit:Lorenz], and symbolic dynamics [@Cit:symb] to name a few. For a broad overview of the theoretical approaches to dynamical systems, we refer the reader to [@Cit:Gucken]. Although, dynamical systems theory has found wide application in engineering and the sciences, it has received scant attention from the computer science community.

Local continuous optimization techniques such as Nesterov’s method [@Cit:Nesterov] have recently been analyzed from a dynamical systems perspective [@Cit:boyd_candes]. Nesterov’s method is an optimal gradient descent algorithm in terms of convergence rate. In [@Cit:boyd_candes], the authors derive a dynamical system by invoking a continuous time limit of the optimization step size. They then analyze the resulting ordinary differential equations (ODEs) to provide valuable insight into the algorithm and its associated optimality. Additionally, in [@Cit:wibisono] the authors use calculus of variations to gain additional insight into the convergence rates of accelerated gradient descent schemes. Although, this body of work does fall under the category of novel application of dynamical systems theory to optimization methods, we will not discuss it at length in this paper for two reasons a) this work has sparked extensive follow-on work and consequently, various summary articles 