29 citations · 203 across the 30 of their papers we have counts for
21 papers · 1 filter
Contact Geometry of Relativistic Particle Motion
Begum Atesli, Ogul Esen, Michal Pavelka
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamic…
Conformal and Contact Kinetic Dynamics and Their Geometrization
Oğul Esen, Ayten Gezici, Miroslav Grmela +3
We propose a conformal generalization of the reversible Vlasov equation of kinetic plasma dynamics, called conformal kinetic theory. In order to arrive at this formalism, we start…
Direct Poisson neural networks: Learning non-symplectic mechanical systems
Martin Šípka, Michal Pavelka, Oğul Esen +1
In this paper, we present neural networks learning mechanical systems that are both symplectic (for instance particle mechanics) and non-symplectic (for instance rotating rigid bod…
A Discrete Hamilton--Jacobi Theory for Contact Hamiltonian Dynamics
Oğul Esen, Cristina Sardón, Marcin Zajac
In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geo…
Tulczyjew's Triplet with an Ehresmann connection I: Trivialization and Reduction
Oğul Esen, Mahmut Kudeyt, Serkan Sütlü
We study the trivialization and the reduction of the Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus obtain trivializations…
Cauchy data space and multisymplectic formulation of conformal classical field theories
Ogul Esen, Manuel de León, Cristina Sardón +1
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description…
The globalization problem of the Hamilton-DeDonder-Weyl equations on a local -symplectic framework
Oğul Esen, Manuel de León, Cristina Sardón +1
In this paper we aim at addressing the globalization problem of Hamilton-DeDonder-Weyl equations on a local -symplectic framework and we introduce the notion of {\it locally con…
Hamilton-Jacobi Formalism on Locally Conformally Symplectic Manifolds
Oğul Esen, Manuel de León, Cristina Sardón +1
In this article we provide a Hamilton-Jacobi formalism in locally conformally symplectic manifolds. Our interest in the Hamilton-Jacobi theory comes from the suitability of this th…
On the quest for generalized Hamiltonian descriptions of -flows generated by curl of a vector potential
Oğul Esen, Partha Guha
We study Hamiltonian analysis of three-dimensional advection flow of incompressible nature assuming that dyna…
De Donder Form for Second Order Gravity
Jędrzej Śniatycki, Oğul Esen
We show that the De Donder form for second order gravity, defined in terms of Ostrogradski's version of the Legendre transformation applied to all independent variables, is globall…
A Hamilton-Jacobi formalism for higher order implicit systems
O. Esen, M. de León, C. Sardón
In this paper, we present a generalization of a Hamilton--Jacobi theory to higher order implicit differential equations. We propose two different backgrounds to deal with higher or…
Reduction of a Hamilton-Jacobi equation for nonholonomic systems
Oğul Esen, Manuel de León, Víctor Manuel Jiménez Morales +1
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generali…
A Hamilton-Jacobi theory for implicit differential systems
O. Esen, M. de León, C. Sardón
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, descr…
Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians
Filiz Çağatay-Uçgun, Oğul Esen, Hasan Gümral
We study the Hamiltonian formalisms of the second order degenerate Clèment and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed while arriving at the…
On Integrals, Hamiltonian and Metriplectic Formulations of 3D Polynomial Systems
Oğul Esen, Anindya Ghose Choudhury, Partha Guha
We apply the Darboux integrability method to determine first integrals and Hamiltonian formulations of three dimensional polynomial systems; namely the reduced three-wave interacti…
On Geometry of Schmidt Legendre Transformation
Oğul Esen, Partha Guha
A geometrization of Schmidt-Legendre transformation of the second order Lagrangians is proposed by building a proper Tulczyjew's triplet. The symplectic relation between Ostrograds…
Hamiltonian Coupling of Electromagnetic Field and Matter
Oğul Esen, Michal Pavelka, Miroslav Grmela
Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual…
A hierarchy of Poisson brackets in non-equilibrium thermodynamics
Michal Pavelka, Vaclav Klika, Ogul Esen +1
Reversible evolution of macroscopic and mesoscopic systems can be conveniently constructed from two ingredients: an energy functional and a Poisson bracket. The goal of this paper…
Lagrangian Dynamics on Matched Pairs
Oğul Esen, Serkan Sütlü
Given a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler-Lagr…
Bi-Hamiltonian Structures of Chaotic Dynamical Systems in 3D
Oğul Esen, Anindya Ghose Choudhury, Partha Guha
We study Poisson structures of dynamical systems with three degrees of freedom which are known for their chaotic properties, namely Lü, modified Lü, Chen, and Qi systems. We sh…
Lie Algebra of Hamiltonian Vector Fields and the Poisson-Vlasov Equations
Oğul Esen, Hasan Gümral
We introduce natural differential geometric structures underlying the Poisson-Vlasov equations in momentum variables. We decompose the space of all vector fields over particle phas…