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The subdivision algorithm by Dellnitz and Hohmann for the computation ofinvariant sets of dynamical systems decomposes the relevant region of the statespace into boxes and analyzes the induced box dynamics. Its convergence isproved in an idealized setting, assuming that the exact time evolution of theseboxes can be computed.  In the present article, we show that slightly modified, directlyimplementable versions of the original algorithm are convergent under very mildassumptions on the dynamical system. In particular, we demonastrate thatneither a fine net of sample points nor very accurate approximations of theprecise dynamics are necessary to guarantee convergence of the overall scheme.

Provably convergent implementations of the subdivision algorithm for the computation of invariant objects