15 citations · 37 across the 18 of their papers we have counts for
21 papers
Couplings of -anchored Bundles
Begüm Ateşli, Oğul Esen, Serkan Sütlü
This work develops an algebraic framework for merging two -anchored bundles over the same base manifold, equipped with mutual actions and two twisted cocycle terms, so as to obt…
Constructions of -Lie algebroids
Begüm Ateşli, Oğul Esen, Serkan Sütlü
The paper investigates the construction of Lie algebroids and -Lie algebroids via connections generated by finite families of differential operators and dual sections. We first…
On Geometry of Dissipation in Multiscale Dynamics and Thermodynamics
Begüm Ateşli, Oğul Esen, Miroslav Grmela +1
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gau…
On Product Lie Algebroids, and Collective Motion
Begüm Ateşli, Oğul Esen, Serkan Sütlü
This work explores the geometrical/algebraic framework of Lie algebroids, with a specific focus on the decoupling and coupling phenomena within the bicocycle double cross product r…
[Locally Conformal Higher Order Lagrangian Dynamics
Serdar Çite, Oğul Esen
This work presents higher order Lagrangian dynamics possessing locally conformal character. More concretely, locally conformal higher order Euler-Lagrange equations are written wit…
Dynamics Over Homogeneous Spaces
Filiz Çağatay Uçgun, Oğul Esen, Serkan Sütlü
We present the Euler-Lagrange and Hamilton's equations for a system whose configuration space is a unified product Lie group , for some . By redu…
Discrete Dynamics on Locally Conformal Framework
Oğul Esen, Ayten Gezici, Hasan Gümral
In this paper, we address the globalization problem of discrete Lagrangian and Hamiltonian dynamics in locally conformal framework.
On Non-autonomous Hamiltonian Dynamics, Dual Spaces, and Kinetic Lifts
Begüm Ateşli, Oğul Esen, Manuel de León +1
Vlasov kinetic theory is the dynamics of a bunch of particles flowing according to symplectic Hamiltonian dynamics. More recently, this geometry has been extended to contact Hamilt…
Implicit Contact Dynamics and Hamilton-Jacobi Theory
Oğul Esen, Manuel Lainz Valcázar, Manuel de León +1
In this paper we propose a Hamilton-Jacobi theory for implicit contact Hamiltonian systems in two different ways. One is the understanding of implicit contact Hamiltonian dynamics…
Contact Dynamics versus Legendrian and Lagrangian Submanifolds
Oğul Esen, Manuel Lainz Valcázar, Manuel de León +1
We are proposing Tulczyjew's triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse f…
Matched Pair Analysis of Euler-Poincaré Flow on Hamiltonian Vector Fields
Oğul Esen, Cristina Sardón, Marcin Zajac
In this paper we provide a matched pair decomposition of the space of symmetric contravariant tensors . From this procedure two complementary Lie subalgebr…
On Geometrical Couplings of Dissipation and Curl Forces
Oğul Esen, Partha Guha, Hasan Gümral
In this paper, we present several geometric ways to incorporate gyroscopic and dissipative forces to curl forces. We first present a proper metriplectic geometry. Then, using the H…
On Extensions, Lie-Poisson Systems, and Dissipations
Oğul Esen, Gökhan Özcan, Serkan Sütlü
On the dual space of \textit{extended structure}, equations governing the collective motion of two mutually interacting Lie-Poisson systems are derived. By including a twisted 2-co…
Geometry and solutions of an epidemic SIS model permitting fluctuations and quantization
Oğul Esen, Eduardo Fernández-Saiz, Cristina Sardón +1
Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This…
Matched pair analysis of the Vlasov plasma
Oğul Esen, Serkan Sütlü
We present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these…
Second Order Lagrangian Dynamics On Double Cross Product Groups
Oğul Esen, Mahmut Kudeyt, Serkan Sütlü
We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Base…
Matched pairs of discrete dynamical systems
Oğul Esen, Serkan Sütlü
Matched pairs of Lie groupoids and Lie algebroids are studied. Discrete Euler-Lagrange equations are written for the matched pairs of Lie groupoids. As such, a geometric framework…
On Time-dependent Hamiltonian Realizations of Planar and Nonplanar Systems
Oğul Esen, Partha Guha
In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems. In particular, we generalize the cosymplectic stru…
Reductions of Dynamics on Second Iterated Bundles of Lie Groups
Oğul Esen, Hasan Gümral
We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotang…
Tulczyjew's Triplet for Lie Groups II: Dynamics
Oğul Esen, Hasan Gümral
Taking configuration space as a Lie group, the trivialized Euler-Lagrange and Hamilton's equations are obtained and presented as Lagrangian submanifolds of the trivialized Tulczyje…
Jets, Lifts and Dynamics
Oğul Esen, Hasan Gümral
We show that complete cotangent lifts of vector fields, their decomposition into vertical representative and holonomic part provide a geometrical framework underlying Eulerian equa…