To automatically learn the behavior of trajectories of a map in Non-Linear Dynamics- the Logistic Map, Deep Neural Networks have been trained. Different iterates of the Logistic Map have been generated and models have been fit to them to test the learning capabilities of Neural Networks under such scenario. This paper examines the capability of Neural Networks to learn the dynamics of a system that can be modeled with the Logistic Map. keywords- Non-Linear Dynamics, Deep Learning, Artificial Neural Networks, Physics, Computational Mathematics, Logistic Map