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Božidar Jovanović

Kneza Mihaila 35, 11000 Belgrade, Serbia
Mathematical Institute, SANU


Jovanović B., Jovanovic V.
Heisenberg Model in Pseudo-Euclidean Spaces II
2018, vol. 23, no. 4, pp.  418-437
In the review we describe a relation between the Heisenberg spin chain model on pseudospheres and light-like cones in pseudo-Euclidean spaces and virtual billiards. A geometrical interpretation of the integrals associated to a family of confocal quadrics is given, analogous to Moser’s geometrical interpretation of the integrals of the Neumann system on the sphere.
Keywords: discrete systems with constraints, contact integrability, billiards, Neumann and Heisenberg systems
Citation: Jovanović B., Jovanovic V.,  Heisenberg Model in Pseudo-Euclidean Spaces II, Regular and Chaotic Dynamics, 2018, vol. 23, no. 4, pp. 418-437
Jovanović B.
Invariant Measures of Modified LR and L$+$R Systems
2015, vol. 20, no. 5, pp.  542-552
We introduce a class of dynamical systems having an invariant measure, the modifications of well-known systems on Lie groups: LR and L$+$R systems. As an example, we study a modified Veselova nonholonomic rigid body problem, considered as a dynamical system on the product of the Lie algebra $so(n)$ with the Stiefel variety $V_{n,r}$, as well as the associated $\epsilon$L$+$R system on $so(n)\times V_{n,r}$. In the 3-dimensional case, these systems model the nonholonomic problems of motion of a ball and a rubber ball over a fixed sphere.
Keywords: nonholonomic constraints, invariant measure, Chaplygin ball
Citation: Jovanović B.,  Invariant Measures of Modified LR and L$+$R Systems, Regular and Chaotic Dynamics, 2015, vol. 20, no. 5, pp. 542-552
Dragović V., Gajić B., Jovanović B.
Note on Free Symmetric Rigid Body Motion
2015, vol. 20, no. 3, pp.  293-308
We consider the Euler equations of motion of a free symmetric rigid body around a fixed point, restricted to the invariant subspace given by the zero values of the corresponding linear Noether integrals. In the case of the $SO(n − 2)$-symmetry, we show that almost all trajectories are periodic and that the motion can be expressed in terms of elliptic functions. In the case of the $SO(n − 3)$-symmetry, we prove the solvability of the problem by using a recent Kozlov’s result on the Euler–Jacobi–Lie theorem.
Keywords: Euler equations, Manakov integrals, spectral curve, reduced Poisson space
Citation: Dragović V., Gajić B., Jovanović B.,  Note on Free Symmetric Rigid Body Motion, Regular and Chaotic Dynamics, 2015, vol. 20, no. 3, pp. 293-308
Jovanović B.
Heisenberg Model in Pseudo-Euclidean Spaces
2014, vol. 19, no. 2, pp.  245-250
We construct analogues of the classical Heisenberg spin chain model (or the discrete Neumann system), on pseudo-spheres and light-like cones in the pseudo-Euclidean spaces and show their complete Hamiltonian integrability. Further, we prove that the Heisenberg model on a light-like cone leads to a new example of the integrable discrete contact system.
Keywords: discrete Hamiltonian and contact systems, the Lax representation, complete integrability
Citation: Jovanović B.,  Heisenberg Model in Pseudo-Euclidean Spaces, Regular and Chaotic Dynamics, 2014, vol. 19, no. 2, pp. 245-250
Jovanović B.
Geodesic Flows on Riemannian g.o. Spaces
2011, vol. 16, no. 5, pp.  504-513
We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related class of Riemannian homogeneous spaces having an additional principal bundle structure.
Keywords: noncommutative integrability, geodesic orbit spaces, complexity of homogeneous spaces, fiber bundles
Citation: Jovanović B.,  Geodesic Flows on Riemannian g.o. Spaces, Regular and Chaotic Dynamics, 2011, vol. 16, no. 5, pp. 504-513
Fedorov Y. N., Jovanović B.
Hamiltonization of the generalized Veselova LR system
2009, vol. 14, no. 4-5, pp.  495-505
We revise the solution to the problem of Hamiltonization of the $n$-dimensional Veselova non-holonomic system studied previously in [1]. Namely, we give a short and direct proof of the hamiltonization theorem and also show the trajectorial equivalence of the problem with the geodesic flow on the ellipsoid.
Keywords: nonholonomic systems, integrability, geodesic flows
Citation: Fedorov Y. N., Jovanović B.,  Hamiltonization of the generalized Veselova LR system, Regular and Chaotic Dynamics, 2009, vol. 14, no. 4-5, pp. 495-505
Jovanović B.
Some Multidimensional Integrable Cases Of Nonholonomic Rigid Body Dynamics
2003, vol. 8, no. 1, pp.  125-132
In this paper we study the dynamics of the constrained $n$-dimensional rigid body (the Suslov problem). We give a review of known integrable cases in three dimensions and present their higher dimensional generalizations.
Citation: Jovanović B.,  Some Multidimensional Integrable Cases Of Nonholonomic Rigid Body Dynamics, Regular and Chaotic Dynamics, 2003, vol. 8, no. 1, pp. 125-132

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