Multiple Hamiltonian structures for Volterra and Toda Lattices
Date
Authors
University
Faculty
Σχολή Θετικών και Εφαρμοσμένων Επιστημών
Faculty of Pure and Applied Sciences
Faculty of Pure and Applied Sciences
Department
Τμήμα Μαθηματικών και Στατιστικής
Department of Mathematics and Statistics
Department of Mathematics and Statistics
Abstract
Η διατριβή χωρίζεται σε δύο μέρη. Στο πρώτο μέρος μελετούμε τα ολοκληρώσιμα συστήματα που κατασκεύαστηκαν από τον Bogoyavlensky το 1988. Αυτά τα συστήματα συνδέονται με
απλές Lie άλγεβρες και γενικεύουν το καλά γνωστό Volterra σύστημα. (...μη διαθέσιμη ηλεκτρονική μορφή της περίληψη στην ελληνική γλώσσα)
Results on the Volterra model which is associated to the simple Lie algebra of type An are extended to the Bogoyavlensky-Volterra systems of type Bn, Cn and Dn. In particular, we find Lax pairs, Hamiltonian and Casimir functions and multi-Hamiltonian structures. We also find Lax pairs for the periodic Bogoyavlensky-Volterra systems. Finally, we investigate the Bogoyavlensky- Toda system of type Dn. For this system we verify that the degrees of the higher Poisson brackets coincide with the exponents of the corresponding Lie group. The areas investigated, include recursion operators, higher Poisson brackets and master symmetries.
Results on the Volterra model which is associated to the simple Lie algebra of type An are extended to the Bogoyavlensky-Volterra systems of type Bn, Cn and Dn. In particular, we find Lax pairs, Hamiltonian and Casimir functions and multi-Hamiltonian structures. We also find Lax pairs for the periodic Bogoyavlensky-Volterra systems. Finally, we investigate the Bogoyavlensky- Toda system of type Dn. For this system we verify that the degrees of the higher Poisson brackets coincide with the exponents of the corresponding Lie group. The areas investigated, include recursion operators, higher Poisson brackets and master symmetries.