A NOTE ON SINGULARITIES OF 3-FLOWS IN
In [Ergodic Theory & Dynamical Systems 12 (1992), 233-253], it was proved that diffeomorphisms in satisfy Axiom A. As to however, the geometric Lorenz attractor in [The Hopf Bifurcation and its Application, Applied Mathematical Series, Vol. 19, Springer-Verlag, 1976, 368-381] implies that there exists a vector field X in that has a singularity accumulated by the periodic orbits, which implies X does not satisfy Axiom A. In this paper, we show that singularities of vector fields in accumulated by the periodic orbits are generally the same as in the geometric Lorenz attractor.
Axiom A, dominated splitting.