Ogul Esen

Gebze-Kocaeli 41400, Turkey
Department of Mathematics, Gebze Technical University


Esen O., Jiménez V. M., de León M., Sardón C.
We discuss, in all generality, the reduction of the Hamilton – Jacobi equation for systems subject to nonholonomic constraints and invariant under the action of a group of symmetries.We consider nonholonomic systems subject to both linear and nonlinear constraints and with different positioning of such constraints with respect to the symmetries.
Keywords: Hamilton – Jacobi, theory of reduction, nonholonomic systems; constrained systems, nonlinear constraints, reconstruction, symplectic reduction, Marsden –Weinstein reduction, symmetries
Citation: Esen O., Jiménez V. M., de León M., Sardón C.,  Reduction of a Hamilton – Jacobi Equation for Nonholonomic Systems, Regular and Chaotic Dynamics, 2019, vol. 24, no. 5, pp. 525-559
Esen O., Choudhury A. G., Guha P., Gümral H.
Superintegrable Cases of Four-dimensional Dynamical Systems
2016, vol. 21, no. 2, pp.  175-188
Degenerate tri-Hamiltonian structures of the Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic Lü and Qi systems are superintegrable and admit tri-Hamiltonian structures.
Keywords: first integrals, Darboux polynomials, Jacobi’s last multiplier, 4D Poisson structures, tri-Hamiltonian structures, Shivamoggi equations, generalized Raychaudhuri equations, Lü system and Qi system
Citation: Esen O., Choudhury A. G., Guha P., Gümral H.,  Superintegrable Cases of Four-dimensional Dynamical Systems, Regular and Chaotic Dynamics, 2016, vol. 21, no. 2, pp. 175-188

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