Zobrazeno 1 - 10
of 190
pro vyhledávání: '"Campoamor Stursberg, Rutwig"'
We revisit the nonlinear second-order differential equations $$ \ddot{x}(t)=a(x)\dot{x}(t)^2+b(t)\dot{x}(t) $$ where $a(x)$ and $b(t)$ are arbitrary functions on their argument from the perspective of Lie-Hamilton systems. For the particular choice $
Externí odkaz:
http://arxiv.org/abs/2412.06057
Publikováno v:
J. Phys. A: Math. Theor. 57 (2024) 485203
We propose a generalization of two classes of Lie-Hamilton systems on the Euclidean plane to two-dimensional curved spaces, leading to novel Lie-Hamilton systems on Riemannian spaces (flat $2$-torus, product of hyperbolic lines, sphere and hyperbolic
Externí odkaz:
http://arxiv.org/abs/2407.01500
Publikováno v:
Commun. Nonlinear Sci. Numer. Simulat. 141 (2025) 108452
A new procedure for the construction of higher-dimensional Lie-Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebras and their realization by vector fields. The notion of intrinsic Lie
Externí odkaz:
http://arxiv.org/abs/2406.17479
We particularise the construction of generalised Kac-Moody algebras associated to compact real manifolds to the case of the two-torus $\mathbb T_2$ and the two-sphere ${\mathbb S}^2$. It is shown that these algebras, as well as a Virasoro algebra ass
Externí odkaz:
http://arxiv.org/abs/2406.10548
Publikováno v:
J. Math. Phys. 65 (2024) 081702
We construct a generalised notion of Kac-Moody algebras using smooth maps from the non-compact manifolds ${\cal M}=$SL$(2,\mathbb R)$ and ${\cal M}=$ SL$(2,\mathbb R)/U(1)$ to a finite-dimensional simple Lie group $G$. This construction is achieved t
Externí odkaz:
http://arxiv.org/abs/2406.09845
We provide a classification and explicit formulas for the elements that span the centralizer of Cartan subalgebras of complex semisimple Lie algebras of non-exceptional type in their universal enveloping algebra, and show that these generate polynomi
Externí odkaz:
http://arxiv.org/abs/2406.01958
Publikováno v:
Axioms 13 (2024) 26
It is shown that the complex Bernoulli differential equations admitting the supplementary structure of a Lie-Hamilton system related to the book algebra $\mathfrak{b}_2$ can always be solved by quadratures, providing an explicit solution of the equat
Externí odkaz:
http://arxiv.org/abs/2312.16586
Publikováno v:
J. Phys.: Conf. Ser. 2667 (2023) 012083
The theory of Lie-Hamilton systems is used to construct generalized time-dependent SIS epidemic Hamiltonians with a variable infection rate from the 'book' Lie algebra. Although these are characterized by a set of non-autonomous nonlinear and coupled
Externí odkaz:
http://arxiv.org/abs/2310.02688
Publikováno v:
Journal of Physics: Conference Series 2667 (1), 012037 (2023)
We review some aspects of the Racah algebra $R(n)$, including the closure relations, pointing out their role in superintegrability, as well as in the description of the symmetry algebra for several models with coalgebra symmetry. The connection inclu
Externí odkaz:
http://arxiv.org/abs/2308.12705
Publikováno v:
Journal of Geometry and Physics 203 (2024)105249
We show that the diffeomorphisms of an extended phase space with time, energy, momentum and position degrees of freedom that leave invariant the symplectic 2-form and and a degenerate orthogonal metric dt^2 locally satisfy Hamilton's equations up to
Externí odkaz:
http://arxiv.org/abs/2308.10766