"Vestnik St. Petersburg University. Mathematics"

Series "Mathematics, Mechanics, Astronomy", Issue 1, 2007

CONTENTS
Mathematics
Viktor Aleksandrovich Pliss (dedicated to his 75th birthday) 3
Andreev A.F. On a singular point with one zero characteristic root 7
Basov V.V., Fedotov A.A. Generalized normal forms for two-dimensional systems of ordinary differential equations with linear and quadratic unperturbed parts 13
Bogolyubov A.A. On local topological conjugacy of nonlinear systems in the neighbouhood of invariant surfaces which consists of equilibrium points 34
Ilyin Yu.A. On existence of local-integral manifold of neutral type for essentially nonlinear system of differential equations 43
Kryzhevich S.G. Structural stability of invariant sets of vibro-impact systems 55
Krym V.R., Petrov N.N. The equations of motion of a charged particle in the five dimensional model of the general relativity theory with the nonholonomic four dimensional velocity space 62
Churin Yu.V. On inner points of manifold of equations with singular periodic solutions 71
Burova I.G., Demina A.F. On smooth interpolating splines constraction 75
Zhuk V.V., Pimenov S.Yu. On norms of generalized Abel?Poisson sums 82
Makarov A.A. On one algebraical identity in the theory of B?-splines of the second degree 91
Zuber I.E., Gelig A.H. Invariant stabilization of nonlinear discrete systems 96
Zhenji Tian. The lattice of completely simple subsemigroups of a completely simple semigroup 99
Mechanics
Goncharova A. B. Stress state of the rubber membrane with crack 104
Pasynkova I.A., Sabaneev V.S. The first mathematical models in the theory of an elastic fast spinning shaft 111
Pogrebskaya T.N., Soltakhanov Sh.Kh. The control of chasing a target by the pursuit method as a nonholonomic problem in mechanics 118
Polyakova E.V., Tovstik P.E., Chaikin V.A. Axisymmetric deformation of a shell of revolutionmade of fibres 128
Astronomy
Osipkov L.P., Jiang Zhenglu. Constructing galaxy models with a central density cusp by equipotential method 139
Papers 145
Editorial Board of the Complete Journal.
Editor-in-chief:   L.A.Verbitskaya.
Associate editors:   I.V.Murin, V.N.Troyan.
Editorial board:   N.A.Belyaev, S.G.Inge-Vechtomov, A.G.Morachevsky, V.T.Ryazanov, R.V.Svetlov, L.E.Smirnov, P.E.Tovstik, I.Ya.Froyanov, T.N.Peskova.
Secretary of the board: A.V.Suvorov.
Editorial Board of the Series "Mathematics, Mechanics and Astronomy".
Editor-in-chief :   P.E.Tovstik
Associate editor:   N.N.Petrov
Secretary of the board:   T.V.Voloshinova
Editorial board:   T.A.Agekyan, S.M.Ermakov, G.A.Leonov, N.F.Morozov, I.P.Mysovskikh, V.S.Novoselov, L.A.Petrosyan, V.A.Pliss, N.N.Uraltseva, B.V.Filippov, K.V.Kholshevnikov.
Address of the editorial board:  198504, Peterhof, Universitetsky pr., 28.
Translation of articles for a journal “Vestnik St. Petersburg University Mathematics” is performed by E.A.Gurmuzova.
Editor T.V.Semenova.   Technical editor A.V.Borshcheva
Phones: 328-97-84, 323-76-30, 328-21-64. E-mail: peterhof@rambler.ru