Papers by Pantelis Damianou
Journal of Nonlinear Mathematical Physics, 2009
We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By usi... more 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 second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.
Springer Proceedings in Mathematics & Statistics, 2014
We compute the characteristic polynomials of affine Cartan, adjacency matrices and Coxeter polyno... more We compute the characteristic polynomials of affine Cartan, adjacency matrices and Coxeter polynomials of the associated Coxeter system using Chebyshev polynomials. We give explicit factorization of these polynomials as products of cyclotomic polynomials. Finally, we present several different methods of obtaining the exponents and Coxeter number for affine Lie algebras. In particular we compute the exponents and Coxeter number for each conjugacy class in the case of A (1) n .
Journal of Geometry and Physics, 2015
We construct a large family of evidently integrable Hamiltonian systems which are generalizations... more 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 number of cases a simple change of variables transforms such a system to a quadratic Lotka-Volterra system. We present in detail all such systems in dimensions 4 and 5 and we also give some examples from higher dimensions. This construction generalizes easily to each complex simple Lie algebra.
Frontiers in Physics, 2014
Nonlinear Dynamics, 2000
Nonlinear Dynamics 36: 3–18, 2004. C 2004 Kluwer Academic Publishers. Printed in the Netherlands.... more Nonlinear Dynamics 36: 3–18, 2004. C 2004 Kluwer Academic Publishers. Printed in the Netherlands. ... Classification of Noether Symmetries for Lagrangians with Three ... PA DAMIANOU and C. SOPHOCLEOUS ∗ Department of Mathematics and Statistics, University of Cyprus, PO Box 20537, 1678 Nicosia, Cyprus; ∗Author for correspondence (e-mail: [email protected]) ... Abstract. We classify all possible Noether symmetries of the Euler–Lagrange equations for a Hamiltonian system with three degrees of freedom. We also review the results for the ...
Journal of Nonlinear Mathematical Physics, 2009
We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By usi... more 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 second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.
Applied Mathematics Letters, 2000
We present some results on the symmetry group classification for an autonomous Hamiltonian system... more We present some results on the symmetry group classification for an autonomous Hamiltonian system with three degrees of freedom. The potentials considered are natural, i.e., depend on the position variables only and the symmetries considered are Lie point symmetries. With the exception of the harmonic oscillator or a free particle where the dimension is 24, we obtain all dimensions between 1 and 12, except 8. (~)
Painlevé Equations and Related Topics: Proceedings of the International Conference, Saint Petersburg, Russia, June 17-23, 2011, Aug 31, 2012
Abstract. We examine a class of Lotka–Volterra equations in three and four dimensions which satis... more Abstract. We examine a class of Lotka–Volterra equations in three and four dimensions which satisfy the Kowalevski–Painlevé property. We restrict our attention to Lotka–Volterra systems defined by a skew symmetric matrix. We obtain a complete classification of such systems. The classification is obtained using Painlevé analysis and, more specifically, by the use of Kowalevski exponents. The imposition of certain integrality conditions on the Kowalevski exponents gives the necessary conditions. We also show that the conditions ...
Regular and Chaotic Dynamics, Jun 1, 2011
The same holds true for what brings us back to Riemann surfaces and Abelian varieties: Its-Matvee... more The same holds true for what brings us back to Riemann surfaces and Abelian varieties: Its-Matveev show in 1975 that every hyperelliptic theta function, with properly scaled space and time coordinates as arguments, is a solution to the Korteweg-de Vries equation (the time and space coordinates being thought of as complex). This observation and its generalization to arbitrary theta functions in connection with the Kadomtsev-Petviashvili equation (KP equation) led to very striking new results. The classical Schottky problem, for example, ...
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Arxiv preprint math/0605660, Jan 1, 2006
Abstract: We consider the problem of constructing Poisson brackets on smooth manifolds $ M $ with... more Abstract: We consider the problem of constructing Poisson brackets on smooth manifolds $ M $ with prescribed Casimir functions. If $ M $ is of even dimension, we achieve our construction by considering a suitable almost symplectic structure on $ M $, while, in the case where $ M $ is of odd dimension, our objective is achieved by using a convenient almost cosymplectic structure. Several examples and applications are presented.
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Papers by Pantelis Damianou