Σ' αυτή τη διατριβή, εξετάζουμε την πλήρη αλγεβρική ολοκληρωσιμότητα των εξισώσεων Lotka - Volterra στις τρεις και στις τέσσερις διαστάσεις, που ορίζονται από ένα αντισυμμετρικό πίνακα. Ο στόχος μας είναι η πλήρη ταξινόμηση ...

We construct a large family of Hamiltonian systems which are connected with root systems of complex simple Lie algebras. These systems are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic ...

We devise a new method for producing Hamiltonian systems by constructing the corresponding Lax pairs. This is achieved by considering a larger subset of the positive roots than the simple roots of the root system of a ...

We establish, using a new approach, the integrability of a particular case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems. The technique used is a modification of the so called quadratic ...

We define an integrable Hamiltonian system of Toda type associated with the real Lie algebra so(p,q). As usual there exist a periodic and a non-periodic version. We construct, using the root space, two Lax pair representations ...

We derive team optimality conditions for differential decision systems with nonclassical information structures. The necessary conditions of optimality are given in terms of Hamiltonian system of equations consisting of a ...