scholarly journals Poisson geometry of PI three‐dimensional Sklyanin algebras

2018 ◽  
Vol 118 (6) ◽  
pp. 1471-1500
Author(s):  
Chelsea Walton ◽  
Xingting Wang ◽  
Milen Yakimov
Keyword(s):  
Three Dimensional ◽  
Poisson Geometry ◽  
Sklyanin Algebras

scholarly journals Integrable Deformations and Dynamical Properties of Systems with Constant Population

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1378
Author(s):  
Cristian Lăzureanu
Keyword(s):  
Differential Equations ◽  
Three Dimensional ◽  
Poisson Geometry ◽  
Volterra System ◽  
First Order ◽  
Integrable Deformations ◽  
Dynamical Properties ◽  
Points Of View ◽  
First Order Differential Equations

In this paper we consider systems of three autonomous first-order differential equations x˙=f(x),x=(x,y,z),f=(f1,f2,f3) such that x(t)+y(t)+z(t) is constant for all t. We present some Hamilton–Poisson formulations and integrable deformations. We also analyze the case of Kolmogorov systems. We study from some standard and nonstandard Poisson geometry points of view the three-dimensional Lotka–Volterra system with constant population.

scholarly journals Poisson geometry and representations of PI 4-dimensional Sklyanin algebras

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Chelsea Walton ◽  
Xingting Wang ◽  
Milen Yakimov
Keyword(s):  
Poisson Geometry ◽  
Sklyanin Algebras

scholarly journals Quotients of degenerate Sklyanin algebras

2017 ◽  
Vol 16 (05) ◽  
pp. 1750085 ◽  
Author(s):  
Kevin De Laet
Keyword(s):  
Heisenberg Group ◽  
Hilbert Series ◽  
Three Dimensional ◽  
Central Element ◽  
Sklyanin Algebras ◽  
Sklyanin Algebra

In this paper, it is shown how the Heisenberg group of order 27 can be used to construct quotients of degenerate Sklyanin algebras. These quotients have properties similar to the classical Sklyanin case in the sense that they have the same Hilbert series, the same character series and a central element of degree 3. Regarding the central element of a three-dimensional Sklyanin algebra, a better way to view this using Heisenberg-invariants is shown.

scholarly journals Ideal classes of three-dimensional Sklyanin algebras

2004 ◽  
Vol 276 (2) ◽  
pp. 515-551 ◽  
Author(s):  
Koen de Naeghel ◽  
Michel van den Bergh
Keyword(s):  
Three Dimensional ◽  
Sklyanin Algebras

scholarly journals Three dimensional Sklyanin algebras and Gröbner bases

2017 ◽  
Vol 470 ◽  
pp. 379-419 ◽  
Author(s):  
Natalia Iyudu ◽  
Stanislav Shkarin
Keyword(s):  
Gröbner Bases ◽  
Three Dimensional ◽  
Grobner Bases ◽  
Sklyanin Algebras

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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