arXiv subjects

Gh. Haghighatdoost

Publications and source records attributed to Gh. Haghighatdoost.

11 recordsLinked to original sources

arXiv2026

Classification of Six-dimensional Real Nilpotent Lie Bialgebras of Symplectic Type and their Poisson-Lie Groups

In this paper, we classify all six-dimensional real nilpotent Lie bialgebras of symplectic type. The Poisson structures on all of the related six-dimensional Poisson-Lie groups are obtained. Some new integrable Hamiltonian systems for which the Poisson-Lie group plays the role of a phase space and its dual Lie group plays the role of a symmetry group of the system are obtained.

math-ph↗

arXiv2022

Integrable bi-Hamiltonian systems by Jacobi structure on real three-dimensional Lie groups

By Poissonization of Jacobi structures on real three-dimensional Lie groups $\mathbf{G}$ and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on $\mathbf{G}\otimes \mathbb{R}$.

math-ph↗

arXiv2020

Poisson-Nijenhuis Structure on Lie groupoids from the Invariance's Point of View

In this paper, we introduce right-invariant (similarly, left-invariant) Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called $(Λ, \mathbf{n})-$structures. We present a mutual correspondence between $(Λ,\mathbf{n})-$structures on Lie algebroids with Poisson-Nijenhuis structures $(Π, \mathbf{N})$ on their Lie groupoids under some conditions. Also, we will construct Poisson-Nijenhuis pair groupoids as an example from the invariance's point of view.

math.DG↗

arXiv2020

Jacobi structures on real two- and three-dimensional Lie groups and their Jacobi-Lie systems

Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two- and three-dimensional Lie groups. Also, we study Jacobi-Lie systems on these real low-dimensional Lie groups. Our results are illustrated through examples of Jacobi-Lie Hamiltonian systems on some real two- and three-dimensional Lie groups.

math-ph↗

arXiv2019

Jacobi-Lie Hamiltonian systems on real low-dimensional Jacobi-Lie groups and their Lie symmetries

We study Jacobi-Lie Hamiltonian systems admitting Vessiot-Guldberg Lie algebras of Hamiltonian vector fields related to Jacobi structures on real low-dimensional Jacobi-Lie groups. Also, we find some examples of Jacobi-Lie Hamiltonian systems on real two- and three- dimensional Jacobi-Lie groups. Finally, we present Lie symmetries of Jacobi-Lie Hamiltonian systems on some three-dimensional real Jacobi-Lie groups.

math-ph↗

arXiv2019

Generalized geometric Hamilton-Jacobi theorem on Lie algebroids

In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi theorem for Hamiltonian system on Lie algebroids. Then this results are generalized and two types of time-dependent Hamilton-Jacobi theorem of Hamiltonian system on Lie algebroids are obtained.

math-ph↗

arXiv2019

Exchanging role of the phase space and symmetry group of integrable Hamiltonian systems related to Lie bialgebras of bi-symplectic types

We construct integrable Hamiltonian systems with Lie bialgebras $({\bf g} , {\bf \tilde{g}})$ of the bi-symplectic type for which the Poisson-Lie groups ${\bf G}$ play the role of the phase spaces, and their dual Lie groups ${\bf {\tilde {G}}}$ play the role of the symmetry groups of the systems. We give the new transformations to exchange the role of phase spaces and symmetry groups and obtain the relations between integrals of motions of these integrable systems. Finally, we give some examples of real four-dimensional Lie bialgebras of bi-symplectic type.

math-ph↗

arXiv2017

On bi-Hamiltonian structure of some superintegrable systems

We discuss bi-Hamiltonian structures for integrable and superintegrable Hamiltonian system on the list of symplectic four-dimensional real Lie groups are classified by G. Ovando. In addition, we creat corresponding control matrix for obtained bi-Hamiltonian structures.

math-ph↗

arXiv2017

Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups

We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way, we calculate some compatible Poisson structures on four dimensional and nilpotent six dimensional symplectic real Lie groups. Then using Magri-Morosi's theorem we obtain new bi-Hamiltonian systems with four dimensional and nilpotent six dimensional symplectic real Lie groups as phase spaces.

math.SG↗

arXiv2017

Classification of four dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups

In this paper we classify all four dimensional real Lie bialgebras of symplectic type. The classical r- matrices for these Lie bialgebras and Poisson structures on all of the related four dimensional Poisson-Lie groups are also obtained. Some new integrable models for which the Poisson-Lie group plays the role as a phase space and its dual Lie group plays the role of a symmetry group of the system, are obtained.

math-ph↗

arXiv2014

Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R4 and R6. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

math-ph↗