title: Checkerboard maps.
abstract: When a map has one positive Lyapunov exponent, its attractors often look like multidimensional, Cantorial plates of spaghetti. What saves the situation is that there is a deterministic jumping from strand to strand. We propose to approximate such attractors as finite sets of K suitably prescribed curves, each parametrized by an interval. The action of the map on each attractor is then approximated by a map that takes a set of curves into itself, and we graph it on a KxK checkerboard as a discontinuous one-dimensional map that captures the quantitative dynamics of the original system when K is sufficiently large. (c) 1995 American Institute of Physics.
authors.affiliation: Department of Astronomy, Columbia University, New York, New York 10027IBM T. J. Watson Laboratories, Yorktown Heights, New York 10598.
authors.forename: N. J.
authors.initials: NJ
authors.lastname: Balmforth
authors.forename: E. A.
authors.initials: EA
authors.lastname: Spiegel
authors.forename: C.
authors.initials: C
authors.lastname: Tresser