Geodesic
Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
V. Khatskevich 1   ; L. Zelenko 2
1 Department of Mathematics ORT Braude Academic College P.O. Box 78, 21982 Karmiel, Israel
2 Department of Mathematics University of Haifa 31905 Haifa, Israel
Studia Mathematica, Tome 177 (2006) no. 3, pp. 195-210 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature of the indefinite metric.
DOI : 10.4064/sm177-3-1
Keywords: study dichotomous behavior solutions non autonomous linear difference equation hilbert space evolution operator equation continuously invertible corresponding unstable subspace infinite dimension general formulate condition ensuring dichotomy terms sequence indefinite metrics hilbert space construct example difference equation which dichotomous behavior solutions compatible signature indefinite metric

V. Khatskevich  1   ; L. Zelenko  2

1 Department of Mathematics ORT Braude Academic College P.O. Box 78, 21982 Karmiel, Israel
2 Department of Mathematics University of Haifa 31905 Haifa, Israel 
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V. Khatskevich; L. Zelenko. Plus-operators in Krein spaces and dichotomous behavior
 of irreversible dynamical systems with discrete time. Studia Mathematica, Tome 177 (2006) no. 3, pp. 195-210. doi: 10.4064/sm177-3-1

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