New additional equations for the Newtonian dynamical systems on Riemannian manifolds are found. They supplement the previously found weak normality conditions up to the complete normality conditions for Newtonian dynamical systems.

The purpose of this article is to describe some basic problems related to the interplay between Dynamical Systems and Mathematical Physics. Since it is impossible to be exhaustive in these topics, we choose to focus on water waves models. These mathematical models are described by partial differential equations that can be understood as dynamical systems in a suitable infinite-dimensional phase...

In this thesis I present the concept of a guided dynamical system, and then I exploit this idea to solve various problems in functional equations and partial differential equations. The results presented here are in a sense a sequel to a series of papers by B. Paneah published in the years 1997-2004. The last chapter in this work is an introduction containing an overview of this work and a comp...