Prof. Dr. Oğul ESEN
Mathematics

Oğul ESEN
Phone
+90 (262) 605 1386
Email
oesen@gtu.edu.tr
Office
Business Administration Building, Z 42
Areas of interest
Geometric Mechanics

Papers

2025

  • Esen, O., Gezici A., Grmela M., Gümral H., Pavelka M., and Sütlü S. (2025) Conformal and contact kinetic dynamics and their geometrization.  Journal of Geometry and Physics 209: 105369.
  • Ateşli, B., Esen, O., de León, M., and Sardón C. (2025) On non-autonomous Hamiltonian dynamics, dual spaces, and kinetic lifts, Physica D: Nonlinear Phenomena 472: 134504.
  • Çağatay Uçgun, F., Esen, O., and Sütlü S. (2025), Dynamics over cocycle double cross-products, International Journal of Geometric Methods in Modern Physics, 10.1142/S0219887825500367.

2024

  • Esen, O., Gezici A., and Gümral H. (2024) Variational aspect and kinetic theory of locally conformal dynamics.  Journal of Physics A: Mathematical and Theoretical 57, no. 36: 365201.
  • Esen, O., Gezici A., and Gümral H. (2024) Discrete Dynamics on Locally Conformal Framework, Proceedings of the Institute of Mathematics and Mechanics, Volume 50, Number 1, 2024, Pages 133–151.
  • Esen, O., Sardón C., and Zajac, M. (2024) A Discrete Hamilton–Jacobi Theory for Contact Hamiltonian Dynamics, Mathematics 2024, 12(15), 234.

2023

  • Esen, O., Valcázar, M. L., de León, M., Sardón, C. (2023). Implicit contact dynamics and Hamilton-Jacobi theory. Differential Geometry and its Applications, 90, 102030.
  • Šípka, M., Pavelka, M., Esen, O., Grmela, M. (2023). Direct Poisson neural networks: Learning non-symplectic mechanical systems. arXiv preprint arXiv:2305.05540.
  • Ajji, A., Chaouki, J., Esen, O., Grmela, M., Klika, V., Pavelka, M. (2023). On geometry of multiscale mass action law and its fluctuations. Physica D: Nonlinear Phenomena, 445, 133642.
  • Ateşli, B., Esen, O., de León, M., Sardón, C. (2023). On locally conformally cosymplectic Hamiltonian dynamics and Hamilton–Jacobi theory. Journal of Physics A: Mathematical and Theoretical, 56(1), 015204.
  • Esen, O., Guha, P., Sütlü, S. (2023). Bicocycle double cross constructions. Journal of Algebra and Its Applications, 22(12), 2350254.
  • Esen, O., Kudeyt, M., Sütlü, S. (2023). Tulczyjew’s triplet with an Ehresmann connection I: Trivialization and reduction. International Journal of Geometric Methods in Modern Physics, 20(04), 2350059.

2022

  • Esen, O., Grmela, M., Pavelka, M. (2022). On the role of geometry in statistical mechanics and thermodynamics. I. Geometric perspective. Journal of Mathematical Physics, 63(12).
  • Esen, O., Grmela, M., Pavelka, M. (2022). On the role of geometry in statistical mechanics and thermodynamics. II. Thermodynamic perspective. Journal of Mathematical Physics, 63(12).
  • Esen, O., de León, M., Lainz, M., Sardón, C., Zajac, M. (2022). Reviewing the geometric Hamilton–Jacobi theory concerning Jacobi and Leibniz identities. Journal of Physics A: Mathematical and Theoretical, 55(40), 403001.
  • Esen, O., Fernández‐Saiz, E., Sardón, C., Zajac, M. (2022). A generalization of a SIS epidemic model with fluctuations. Mathematical Methods in the Applied Sciences, 45(7), 3718-3731.
  • Esen, O., J De Lucas, CS Muñoz, M Zajac, (2022). Decomposing Euler–Poincaré Flow on the Space of Hamiltonian Vector Fields, Symmetry 15 (1), 23.
  • Ateşli, B., Esen, O., Sütlü, S. (2022). Cohomologies and generalized derivations of n-Lie algebras. New York J. Math, 28, 1637-1655.
  • Esen, O., Guha, P., Gümral, H. (2022). 3D-flows generated by the curl of a vector potential and Maurer-Cartan equations. Turkish Journal of Mathematics, 46(8), 3234-3244.
  • Esen, O., Özcan, G., Sütlü, S. (2022). On Extensions, Lie-Poisson Systems, and Dissipation. Journal of Lie Theory, 32(2), 327-382.

2021

  • Esen, O., de León, M., Sardón, C., Zajac, M. (2021). The Globalization Problem of the Hamilton–DeDonder–Weyl Equations on a Local k-Symplectic Framework. Mediterranean Journal of Mathematics, 18(1), 1-25.
  • Esen, O., de León, M., Sardón, C.,Zajac, M. (2021). Cauchy data space and multisymplectic formulation of conformal classical field theories. Annals of Physics, 434, 168616.
  • Esen, O., Kudeyt, M., Sütlü, S. (2021). Second order Lagrangian dynamics on double cross product groups. Journal of Geometry and Physics, 159, 103934.
  • Vágner, P., Pavelka, M., Esen, O. (2021). Multiscale thermodynamics of charged mixtures. Continuum Mechanics and Thermodynamics, 33(1), 237-268.
  • Esen, O., Sütlü, S. (2021). Matched pair analysis of the Vlasov plasma. Journal of Geometric Mechanics, 13(2), 209.
  • Esen, O., de León, M., Sardón, C., Zajac, M. (2021). Hamilton–Jacobi formalism on locally conformally symplectic manifolds. Journal of Mathematical Physics, 62(3), 033506.
  • Esen, O., Sütlü, S. (2021). Discrete dynamical systems over double cross-product Lie groupoids. International Journal of Geometric Methods in Modern Physics, 18(04), 2150057.
  • Esen, O., Kudeyt, M., Sütlü, S. (2021). Second order Lagrangian dynamics on double cross product groups. Journal of Geometry and Physics, 159, 103934.
  • Esen, O., Lainz Valcázar, M., de León, M., Marrero, J. C. (2021). Contact dynamics: Legendrian and Lagrangian submanifolds. Mathematics, 9(21), 2704.
  • Esen, O., Özcan, G., Sütlü, S. (2021). Sönümlemeli sistemlerin eşlenmesi üzerine. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 21(2), 273-282.
  • Esen, O., Kaya, H. K., Sütlü, S. (2021). Lie Cebiroidleri Üzerindeki Lagrange Dinamiğinin Eşlenmesi Problemi Üzerine. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25(2), 162-171.
  • Esen, O., Kudeyt, M., Sütlü, S. (2021). Eşlenmiş Lie Grupları Üzerindeki Lagrange Fark Denklemleri. International Journal of Advances in Engineering and Pure Sciences, 33(2), 250-258.
  • Ateşli, B., Esen, O., Sütlü, S. (2021). Epidemiyolojideki Kompartman Modellerinin Eşlenmiş Hamilton Analizi. International Journal of Advances in Engineering and Pure Sciences, 33(2), 265-276.

2020

  • F. Çağatay Uçgun, O. Esen and H. Gümral (2020) Reductions of Topological Massive Gravity II: First Order Realizations of Second Order Lagrangians,Journal of Mathematical Physics 61, 073504.
  • Esen, O., Guha, P. (2020). On the quest for generalized Hamiltonian descriptions of 3D-flows generated by the curl of a vector potential. International Journal of Geometric Methods in Modern Physics, 17(03), 2050042.

2019

  • Esen, O., Jiménez V. M., de León M., Sardón C., (2019) Reduction of a Hamilton – Jacobi Equation for Nonholonomic Systems, Regular and Chaotic Dynamics, vol.24, no. 5, pp.525-559.
  • Esen, O., Han, D., Şengül T., Wang, Q., (2019). On the nonlinear stability and the existence of selective decay states of 3D quasi‐geostrophic potential vorticity equation. Mathematical Methods in the Applied Sciences, 43(2), 822-846.
  • Esen, O., C Grmela, M., Gümral, H., Pavelka, M. (2019) Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy. Entropy, 21, 907.
  • Esen, O., de León, M., J., Sardón, C. (2019) A Hamilton-Jacobi formalism for higher order implicit systems. A Hamilton–Jacobi formalism for higher order implicit Lagrangians. Journal of Physics A: Mathematical and Theoretical, 53(7), 075204.
  • Śniatycki, J., Esen, O., (2019). De Donder form for second order gravity. Journal of Geometric Mechanics, 12(1), 85.

2018

  • F. Çağatay Uçgun, O. Esen and H. Gümral (2018) Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians,Journal of Mathematical Physics; Volume 59, Issue 1, 10.1063/1.5021948.
  • O. Esen, Guha, P. (2018). On time-dependent Hamiltonian realizations of planar and nonplanar systems, Journal of Geometry and Physics,10.1016/j.geomphys.2018.01.024
  • O. Esen, M. de León, and C. Sardón (2018), A Hamilton-Jacobi theory for implicit differential systems, Journal of Mathematical Physics 59, 022902,
  • O. Esen, Guha, P. (2018) On the geometry of the Schmidt-Legendre transformation. Journal of Geometric Mechanics, 2018, 10 (3) : 251-291

2017

  • O. Esen and S. Sütlü, (2017), Lagrangian Dynamics on Matched Pairs, Journal of Geometry and Physics, Volume 111, Pages 142–157.
  • O. Esen, M. Pavelka, M. Grmela (2017), Hamiltonian coupling of electromagnetic field and matter, Int J Adv Eng Sci Appl Math, DOI 10.1007/s12572-017-0179-4.
  • O.Esen and H. Gümral, (2017), Tulczyjew's Triplet for Lie Groups II: Journal of Lie Theory, Journal of Lie Theory 27, No. 2, 329--356.
  • O. Esen, A. G. Choudhury and P. Guha, (2017) On Integrals, Hamiltonian and Metriplectic Formulations of 3D Polynomial Systems, Theoretical and Applied Mechanics, 44 (1), 15-34.
  • O. Esen, (2017), Dinamik Sistemlerin Eşlenmesi, Sakarya Üni. Fen Bilimleri Enstitüsü dergisi 21 (3), 469-480.

2016

  • O. Esen, A. G. Choudhury, P. Guha, H. Gümral, (2016), Superintegrable Cases of Four-Dimensional Dynamical Systems, Regular and Chaotic Dynamics, Vol 21, Issue 2, pp. 175-188160;
  • M. Pavelka, V. Klika, O. Esen and M. Grmela, (2016), A hierarchy of Poisson brackets in non-equilibrium thermodynamics, Physica D Volume 335, Pages 54–69.
  • O. Esen and S. Sütlü, (2016), Hamiltonian Dynamics on Matched Pairs, International Journal of Geometric Methods in Modern Physics, Int. J. Geom. Methods Mod. Phys. 13, 1650128.
  • O. Esen, A. G. Choudhury and P. Guha, (2016) Bi-Hamiltonian Structures of 3D Chaotic Dynamical Systems, International Journal of Bifurcation and Chaos. Volume 26, Issue 13, 1650215.

2015

  • O.Esen and H. Gümral, (2015), Reductions of Dynamics on Second Iterated Bundles of Lie Groups arXiv:1503.06568.

2014

  • O. Esen and H. Gümral, (2014), "Tulczyjew's Triplet for Lie Groups I: Trivializations and Reductions", Journal of Lie Theory, Volume: 24, pp. 1115-1160.

2013

  • O. Esen ve H. Gümral, (2013), Kontakt Parçacıkların Kinetik Denklemleri, XVII. Ulusal Mekanik Kongresi Bildiriler Kitabı, sf. 370-378.

2012

  • O. Esen and H. Gümral, (2012), Geometry of Plasma Dynamics: Lie algebra of Hamiltonian vector fields, Journal of Geometric Mechanics, Volume: 4 Issue: 3, pp. 239-269.;
  • O. Esen and H. Gümral, (2012), Lie Algebra of Hamiltonian Vector Fields and Poisson-Vlasov Equations, arXiv: 1203.1437.

2011

  • O. Esen and H. Gümral, (2011), Lifts, Jets and Reduced dynamics, International Journal of Geometric Methods in Modern Physics, Volume: 8, Issue: 2, pp. 331-344.

2010

  • O. Esen, (2010), Taşınım, Ayrışım ve Momentum Vlasov denklemleri, XVI. Ulusal Mekanik Kongresi Bildiriler Kitabı, sf. 581-590.

Ph.D. Thesis (Completed. 2017) Filiz Çağatay Uçgun, On geometry of degenerate second order Lagrangians. (YU)

Ph.D. Thesis, (Completed. 2024) Begüm Ateşli, On (de)couplings of Lie type structures. (GTU)

Ph.D. Thesis, Ayten Gezici, (ongoing), GTU

MS Thesis,(Completed. 2023) Tuğba Davşan, On nonholonomic dynamics (GTU)

  • Third Cycle (Doctoral): Yeditepe University, 2010
  • Second Cycle (Master's): Yeditepe University, 2006
  • First Cycle (Undergraduate): Boğaziçi University, 2002
Projects

TUBİTAK 3501: 117F426: Proje yöneticisi ve araştırmacısı: Eşlenmiş Lagrange Ve Hamilton Sistemleri (2018-2021)