On uniqueness criteria for systems of ordinary differential equations (Q1399317)

A local equivalence between two initial value problems is used to prove a uniqueness criterion for the classical Cauchy problem. Moreover, a version of Lipschitz's uniqueness criterion is generalized. Finally, it is proved that continuity implies local uniqueness for a class of two-dimensional autonomous systems, which includes the Hamiltonian ones, provided that the initial condition is not a critical point.