Checkerboard maps.
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.
Balmforth
N. J.
NJ
Department of Astronomy, Columbia University, New York, New York 10027IBM T. J. Watson Laboratories, Yorktown Heights, New York 10598.
Spiegel
E. A.
EA
Tresser
C.
C