Geodesic
Approximation of attractors for evolution equations with the help of attractors for finite systems
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 23, Tome 197 (1992), pp. 71-86

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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. 
@article{ZNSL_1992_197_a3,
     author = {I. N. Kostin},
     title = {Approximation of attractors for evolution equations with the help of attractors for finite systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {71--86},
     publisher = {mathdoc},
     volume = {197},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a3/}
}
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I. N. Kostin. Approximation of attractors for evolution equations with the help of attractors for finite systems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 23, Tome 197 (1992), pp. 71-86. http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a3/