"On some aspects of the geometry of differential equations in physics"


In this review paper, we consider three kinds of systems of differential
equations, which are relevant in physics, control theory and other
applications in engineering and applied mathematics; namely: Hamilton
equations, singular differential equations, and partial differential
equations in field theories.
The geometric structures underlying these systems are presented and
commented.
The main results concerning these structures are stated and discussed,
as well as their influence on the study of the differential equations
with which they are related.
Furthermore, research to be developed in these areas is also commented.