Hamiltonsche Bahnen ohne Zerspaltungseigenschaft. Die Loesung einer Aufgabe von M. G. Krein
| dc.creator | Choroszavin, Sergej A. | |
| dc.date | 1999-08-30 | |
| dc.date | 2002-11-24 | |
| dc.date.accessioned | 2026-07-07T05:30:35Z | |
| dc.date.available | 2026-07-07T05:30:35Z | |
| dc.description | There are constructed linear Hamiltonian (dynamical) systems such that their no nonzero trajectory has usual asymptotical dichotomy property. In particular there is solved (in the negative) one of the so-called M. G. Krein problem. In fact Definition: Let J be period-2 unitary operator and U be linear operator. If U^*JU = UJU^* = J then U is said to be J-unitary. KREIN Problem: given a J-unitary operator U, does there exist an U-invariant subspace L, say, with r(U|L)\leq1 ? In the special case that the operator U^*U-I is compact this problem was solved in the positive by M.G.Krein in 1964. We shall show that, by contrast, in the general case such a subspace L needs not exist. Moreover, there asserts Theorem: For every real c>0 there exists some J-unitary operator U such that (i) if L is some nonzero U-invariant subspace, then r(U|L)>c; (ii) if L' is some nonzero U^{-1}-invariant subspace, then r(U^{-1}|L')>c; This result applies both to the real space case and to the complex space case. In addition, one can assume that U is linear symplectic automorphism. A similar result is obtained for the case of continuous 'dynamic' and for the question: does there exist a nonzero quasistable manifold? | |
| dc.description | introduction, background and comments are extended, several propositions are added, Latex 2.09, in German, Journal-ref, e-mail: izvraen@ssu.samara.ru, http://www.mnu.samara.ru/~journal | |
| dc.identifier | https://arxiv.org/abs/math/9908169 | |
| dc.identifier | http://arxiv.org/abs/math/9908169 | |
| dc.identifier | TRANSECTIONS of RANS, series MMMIC, 1997, v.1, N 2, 95-101 TRANSECTIONS of RANS, series MMMIC, 1998, v.2, N 2, 97-103 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79035 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | Representation Theory | |
| dc.subject | Spectral Theory | |
| dc.title | Hamiltonsche Bahnen ohne Zerspaltungseigenschaft. Die Loesung einer Aufgabe von M. G. Krein | |
| dc.type | text |