Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations

This study deals mainly with the relevance of integral manifolds associated with a Lie algebra with singularities for studying systems of first order partial differential equations, stochastic differential equations and nonlinear control systems. The analysis is based on the algebraic representation of gradient systems in a Lie algebra, allowing the recovery of the original vector fields and the associated Lie algebra as well. Special attention is paid to nonlinear control systems encompassing specific problems of this theory and their significance for stochastic differential equations. The work is written in a self-contained manner, presupposing only some basic knowledge of algebra, geometry and differential equations. This volume will be of interest to mathematicians and engineers working in the field of applied geometric and algebraic methods in differential equations. It can also be a supplementary text for postgraduate students.