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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. LOMI, 1992 Volume 197, Pages 71–86 (Mi znsl5061)

Approximation of attractors for evolution equations with the help of attractors for finite systems

I. N. Kostin


Abstract: The problem of approximation of attractors for semidynamical systems (SDS) in a metric space is considered. Let some (exact) SDS possessing an attractor $M$ be inaccurately defined, i.e. another SDS, which is close in some sense to the exact one be given. The problem is to construct a set $\widetilde{M}$, which is close to $M$ in Hausdorff metric. A finite procedure for construction of $\widetilde{M}$ is suggested. The obtained results are suitable for numerical construction of attractors for rather large class of systems, including one generated by the Lorenz equations.

UDC: 517.962.8


 English version:
Journal of Mathematical Sciences, 1995, 75:6, 2028–2037

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