All results on problems of iterated roots, as we have known, almost only deal with the differentiability at a fixed point, but for two fixed points (even for two fixed end points) we have no conclusions. In this paper...All results on problems of iterated roots, as we have known, almost only deal with the differentiability at a fixed point, but for two fixed points (even for two fixed end points) we have no conclusions. In this paper we discuss the self-homeomorphism on a closed interval with only two fixed points at the two end points of this interval. An exciting result on the variability of the local uniqueness under a small local perturbation is given, and further we see that the iterated roots which are differentiable at both end points of the interval are extremely little.展开更多
文摘All results on problems of iterated roots, as we have known, almost only deal with the differentiability at a fixed point, but for two fixed points (even for two fixed end points) we have no conclusions. In this paper we discuss the self-homeomorphism on a closed interval with only two fixed points at the two end points of this interval. An exciting result on the variability of the local uniqueness under a small local perturbation is given, and further we see that the iterated roots which are differentiable at both end points of the interval are extremely little.
