• Article  

      Bogoyavlensky-Volterra and Birkhoff integrable systems 

      Damianou, Pantelis A.; Kouzaris, S. P. (2004)
      In this paper we examine an interesting connection between the generalized Volterra lattices of Bogoyavlensky and a special case of an integrable system defined by Sklyanin. The Sklyanin system happens to be one of the ...
    • Article  

      Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices 

      Damianou, Pantelis A. (2004)
      This paper is mainly a review of the multi-Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include ...
    • Article  

      The negative relativistic toda hierarchy and rational poisson brackets 

      da Costa, J. M. N.; Damianou, Pantelis A. (2004)
      We define hierarchies for negative values of the index of Poisson tensors, master symmetries and Hamiltonians for the finite, nonperiodic, relativistic Toda lattice. We show that the usual relations between master symmetries, ...
    • Article  

      The negative Toda hierarchy and rational Poisson brackets 

      Damianou, Pantelis A. (2003)
      In this paper we extend the usual hierarchies for the finite, nonperiodic Toda lattice for negative values of the index. We define an infinite sequence of rational homogeneous Poisson brackets, master symmetries, invariants ...
    • Article  

      Noether and master symmetries for the Toda lattice 

      Damianou, Pantelis A.; Sophocleous, Christodoulos (2005)
      In this letter we examine the interrelation between Noether symmetries, master symmetries and recursion operators for the Toda lattice. The topics include invariants, higher Poisson brackets and the various relations they ...
    • Article  

      So (p, q) Toda systems 

      Charalambides, Stelios A.; Damianou, Pantelis A. (2013)
      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 ...
    • Article  

      The Toda lattice is super-integrable 

      Agrotis, Maria A.; Damianou, Pantelis A.; Sophocleous, Christodoulos (2006)
      We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2 N - 1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient ...