Existence of solutions entering at a singular point of an autonomous system having a formal solution (Q754025)

For the investigation of the neighbourhood of the singular point \(x=0\) of the system \(\dot x=f(x)\) \((f(0)=0)\) it is important to find the solutions which enter (or leave) that point. One possible approach to this problem is to construct a formal solution which belongs to a class of series for which a general existence result is known. Our aim is to obtain such a result for series which consist of real powers of t, of iterated logarithms of t and of iterated exponentials of t.