invariants of the integrable hamiltonian systems,
problem of global extremum.
UDC:
514.745.82, 513.944, 517.938.5, 517.946
Subject:
topology of the integrable hamiltonian systems, optimal control theory
Main publications:
O. E. Orel, “A criterion for orbital equivalence of integrable Hamiltonian systems in the vicinity of elliptic orbits. An orbital invariant in the Lagrange problem”, Mat. Sb., 188:7 (1997), 139–160; Sb. Math., 188:7 (1997), 1085–1105
O. E. Orel, P. E. Ryabov, “Bifurcation sets in a problem on motion of a rigid body in fluid and in the generalization of this problem”, Regul. Chaotic Dyn., 3:2 (1998), 82–91
O. E. Orel, “Rotation function for integrable problems reducing to the Abel equations. Orbital classification of Goryachev–Chaplygin systems.”, Sb. Math., 186:2 (1995), 271–296
3.
O. E. Orel, S. Takahashi, “Orbital classification of the integrable problems of Lagrange and Goryachev–Chaplygin by the methods of computer analysis”, Sb. Math., 187:1 (1996), 93–110
4.
O. E. Orel, “The Euler problem in solid body dynamics and the Jacobi problem about geodesics on an ellipsoid are not topologically conjugate”, Math. Notes, 61:2 (1997), 206–211
5.
O. E. Orel, “A criterion for orbital equivalence of integrable Hamiltonian systems in the vicinity of elliptic orbits. An orbital invariant in the Lagrange problem”, Sb. Math., 188:7 (1997), 1085–1105
6.
O. E. Orel, “Rotation functions in the problem of orbit classification of geodesic flows of ellipsoids and in the Euler problem of the dynamics of a rigid body”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 1, 24–32
7.
O. E. Orel, “Topological analysis of a neighbourhood of a degenerate one-dimensional orbit of the Poisson action of $\mathbb R^2$ on the symplectic manifold $M^4$”, Russian Math. Surveys, 48:3 (1993), 176–177
8.
J. Math. Sci. (New York), 94:2 (1999), 1230–1236
9.
O. E. Orel, “Investigation of a neighborhood of a degenerate one-dimensional orbit of the Poisson action of $\mathbb R^2$ in $M^4$”, Proc. Steklov Inst. Math., 205 (1995), 103–118
10.
O. E. Orel, “Algebro-geometricheskie skobki Puassona v probleme tochnogo integrirovaniya”, Regul. Chaotic Dyn., 2:2 (1997), 90–97
11.
O. E. Orel, “The integrable Euler and Jacobi problems are not topologically
conjugate”, Dokl. Akad. Nauk, 354:3 (1997), 307–309
