Geodesic
A dynamical system in a Hilbert space with a weakly attractive nonstationary point
Mathematica Bohemica, Tome 118 (1993) no. 4, pp. 401-423.

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A differential equation is a Hilbert space with all solutions bounded but with so finite nontrivial invariant measure is constructed. In fact, it is shown that all solutions to this equation converge weakly to the origin, nonetheless, there is no stationary point. Moreover, so solution has a non-empty $\Omega$-set.
DOI : 10.21136/MB.1993.126159
Classification : 34D99, 34F05, 34G20, 60H15
Keywords: invariant measures; stochastic evolution equations; Hilbert space; compact semigroup; Galerkin approximation; differential equations in Hilbert spaces; $\Omega$-sets 
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Vrkoč, Ivo. A dynamical system in a Hilbert space with a weakly attractive nonstationary point. Mathematica Bohemica, Tome 118 (1993) no. 4, pp. 401-423. doi : 10.21136/MB.1993.126159. http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.126159/

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