Algebraic integrability of Lotka Volterra equations in three and four dimensions
In this thesis we examine the algebraic integrablility of Lotka-Volterra systems in three and four dimensions. We restrict attention to systems defined by a skew-symmetric matrix. The basic tool in the classification is the use of Painleve analysis, examination of the eigenvalues of the Kowalevski matrix and other standard Lax pair and Poisson techniques. Some number theoretic techniques are also used.