Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonsche Bahnen ohne Zerspaltungseigenschaft. Die Loesung einer
  Aufgabe von M. G. Krein   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?

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The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph