Method of constructing exactly solvable chaos

Details Method of constructing exactly solvable chaos Method of constructing exactly solvable chaos

May 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phrve..55.5280u&link_type=abstract

Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics), Volume 55, Issue 5, May 1997, pp

Physics

19

Scientific paper

We present a systematic method of constructing rational mappings as ergodic transformations with nonuniform invariant measures on the unit interval I=[0,1]. As a result, we obtain a two-parameter family of rational mappings that have a special property in that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is shown here that this family is the most generalized class of rational mappings possessing the property of exactly solvable chaos on I, including the Ulam-von Neumann map y=4x(1-x). Based on the present method, we can produce a series of rational mappings resembling the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction, and we can match some rational functions with other experimentally obtained first return maps in a systematic manner.

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