Many questions in natural science and engineering are transformed into nonlinear equations to be found

Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point.The property of chaos serials produced by one dimensional simple chaotic mapping method with infinite collapses and even symmetry in finite interval was analyzed.For the first time

a new method to find all solutions based on utilizing one dimensional chaotic mapping method with infinite collapses and even symmetry to obtain locate initial points to find all solutions of the nonlinear questions was proposed.The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.