19-23 June 2023
Faculty of Physics, University of Warsaw
Europe/Warsaw timezone
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Darboux polynomials


Location: Faculty of Physics, University of Warsaw
Address: Pasteura 5, Warsaw
Room: Lecture hall: 0.06
Date: 22 Jun 16:30 - 18:20

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Displaying 4 contributions out of 4
Celledoni et al [1,2] have illustrated the power of using so-called Darboux polynomials to search for preserved integrals and measures of a rational map L (including a map arising as a Kahan-Hirota-Kimura discretisation of a (Hamiltonian) ODE). For instance, integrals are obtained as the ratio of two Darboux polynomials where each Darboux polynomial satisfies an equation of the form P(x') = C(x) ... More
Presented by Prof. John ROBERTS on 22/06/2023 at 15:00
We will discuss (mainly linear) Darboux polynomials for ODEs and for difference equations, and show their relation to the preservation of measures and first integrals, and in the construction of integrable systems.
Presented by Prof. Reinout QUISPEL on 22/06/2023 at 14:30
The motivation of our research is to find structure preserving discretizations of dynamical systems by developing some ideas related to the method of discrete gradients [1]. First, we recall that the discrete gradient method can be improved in two different ways without losing the energy conservation property, either by increasing its order [2], or by so-called locally exact discretizations that ... More
Presented by Jan CIEśLIńSKI on 22/06/2023 at 16:00
The Kahan discretization of a Lotka-Volterra system leads to a rational map parametrized by the step size. When this map is Poisson with respect to the quadratic Poisson structure of the Lotka-Volterra system we say that this system has the Kahan-Poisson property. There is a well known family of Lotka-Volterra systems having the Kahan-Poisson property. Their underlying graph has n vertices 1, 2, . ... More
Presented by Dr. Charalampos EVRIPIDOU on 22/06/2023 at 15:30
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