On eliminability of singularities in one-dimension dynamic systems

We discuss correct statement of problems of removability of dynamic systems singularities. Using the structural stability concept some ways for construction of possible perturbations classes are offered. For the case of one phase variable for singularities definied by (N + 1)-th order zero of the righthand part, theorems of singularities unremovability in families with the number of parameters not smaller than N are presented. As the main result of the work we prove that in the case when the number of parameters is less then N, there exist invariants which guarantee removability of such singularities.