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, “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
3.
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
4.
O. E. Orel, “Algebro-geometricheskie skobki Puassona v probleme tochnogo integrirovaniya”, Regul. Chaotic Dyn., 2:2 (1997), 90–97
5.
O. E. Orel, “The integrable Euler and Jacobi problems are not topologically
conjugate”, Dokl. Akad. Nauk, 354:3 (1997), 307–309
6.
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
7.
J. Math. Sci. (New York), 94:2 (1999), 1230–1236
8.
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
9.
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
10.
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
11.
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
