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Constructing Permutations that Approximate Lebesgue Measure Preserving Dynamical Systems Under Spatial Discretization
journal contribution
posted on 1997-02-01, 00:00 authored by P E Kloeden, Jamie MustardJamie MustardA discrete-time dynamical system can sometimes display quite different dynamical behavior under spatial discretization. Systems generated by maps for which the Lebesgue measure is invariant are, however, robust in the sense that they can be approximated by permutations on a uniform lattice. A fast algorithm to construct such permutations is presented here and its implementation is illustrated with several examples of well–known one and two dimensional systems.