Foundation of Hamiltonian Systems

In this project we do : - start with the review of the theory of Ordinary Differential Equations (in short ODEs) and study an abstract Cauchy problem (in Banach spaces). - Study linear Systems, the notion of Stability and also consider nonlinear systems, - Introduce Hamiltonian systems in euclidean spaces and Hilbert spaces; - Show the existence of solutions for every finite dimensional autonomous Hamiltonian systems with initial conditions and Hamiltonian H of class C2 with bounded gradient. - Give a result by BENCI on the existence of periodic solutions of Hamiltonian systems (with prescribed energy h) with a regular Hamiltonian.

Autorentext

Soh Edwin Mukiawa ,MS.c in Pure and Applied Mathematics, Bs.c in Mathematics and Computer Science, From Cameroon .Graduate School: African University of Science and Technology Abuja Nigeria(AUST).Undergraduate School :University of Buea Cameroon.Work on a project title :Foundation of Hamiltonian Systems.Presently engaged with AUST for Phd studies