The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.
Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.
Contents: IntroductionGeometric FundamentalsBasics on Lie Systems and Superposition RulesLie–Hamilton SystemsDirac–Lie SystemsJacobi–Lie Systemsκ-symplectic Lie SystemsConformal and Killing Lie Algebras on the PlaneLie Symmetry for Differential Equations
Readership: The book is aimed at Physics and Mathematics students finishing their degree, doctoral students, and researchers.Superposition Rule;Lie System;Jacobi Structure;Symplectic Structure;Poisson Structure;Jacobi Structure;Riemann Structure;Riccati Equation00
