Web graphics for the computation of invariant measures

摘要

For a non-singular mapping S : [0, 1] → [0, 1], let P be the corresponding Frobenius–Perron operator. In the paper, the web-based computation for the fixed density of P is developed by means of utilizing the PHP technology with the GD graph. The endeavor of the paper is to explore the graphic techniques in PHP and GD to provide visual representations for the probability distribution of the chaotic orbits of the transformation. Some online examples also are presented to illustrate the usefulness of the web graphics.