42 citations · 206 across the 23 of their papers we have counts for
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Poisson brackets after Jacobi and Plucker
Pantelis A. Damianou
We construct a symplectic realization and a bi-hamiltonian formulation of a 3-dimensional system whose solution are the Jacobi elliptic functions. We generalize this system and the…
Symmetries of Toda Equations
Pantelis A. Damianou
We find a sequence consisting of time dependent evolution vector fields whose time independent part corresponds to the master symmetries for the Toda equations. Each master symmetr…
Multiple Hamiltonian Structures for Toda-type systems
Pantelis A. Damianou
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simpl…
On generalized Volterra systems
Stelios A. Charalambides, Pantelis A. Damianou, Charalampos A. Evripidou
We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a numbe…
so(p,q) Toda Systems
Stelios A. Charalambides, Pantelis A. Damianou
We define an integrable hamiltonian system of Toda type associated with the real Lie algebra $\so{p}{q}$. As usual there exists a periodic and a non-periodic version. We construct,…
Darboux polynomials for Lotka-Volterra systems in three dimensions
Yiannis T. Christodoulides, Pantelis A. Damianou
We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as…
A symplectic realization of the Volterra lattice
M. A. Agrotis, P. A. Damianou, G. Marmo
We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master s…
Bogoyavlensky--Volterra and Birkhoff Integrable Systems
Pantelis A. Damianou, Stelios P. Kouzaris
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 Sk…
Volterra's realization of the KM-system
M. A. Agrotis, P. A. Damianou
We construct a symplectic realization of the KM-system and obtain the higher order Poisson tensors and commuting flows via the use of a recursion operator. This is achieved by doub…
The Toda lattice is super-integrable
M. Agrotis, P. A. Damianou, C. Sophocleous
We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of…
From the Toda Lattice to the Volterra lattice and back
Pantelis A. Damianou, Rui L. Fernandes
We discuss the relationship between the multiple Hamiltonian structures of the generalized Toda lattices and that of the generalized Volterra lattices. We use a symmtery approach f…