Abstract: 4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits must bring chaos, chaos also bring the complication of the problem on the existence of likely limit sets. We testified the existence of the maps' likely limit sets using the method of fractal geometry and estimated their Hausdorff dimension. In the end, we gave an idiographic example to proof the existence of 4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits.

Key words: Feigenbaum's map, likely limit set, Hausdorff dimension