Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Provably convergent implementations of the subdivision algorithm for the
  computation of invariant objects   The subdivision algorithm by Dellnitz and Hohmann for the computation of
invariant sets of dynamical systems decomposes the relevant region of the state
space into boxes and analyzes the induced box dynamics. Its convergence is
proved in an idealized setting, assuming that the exact time evolution of these
boxes can be computed.
  In the present article, we show that slightly modified, directly
implementable versions of the original algorithm are convergent under very mild
assumptions on the dynamical system. In particular, we demonastrate that
neither a fine net of sample points nor very accurate approximations of the
precise dynamics are necessary to guarantee convergence of the overall scheme.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph