[4] Once, while talking with Lefschetz, Peixoto commented that no one cared about structural stability of dynamical systems and that was the main problem in working with it.

Try to work as hard and as fast as you can on this subject because the day will come when you will not understand a single word of what they will be saying about structural stability; this happened to me in topology.

[4] Back to Princeton, Peixoto met Steve Smale, the mathematician that would later become a reference in dynamical systems.

According to Bunge Foundation, "the theorem of Peixoto on the structural stability in two-dimensional varieties inspired the mathematician S. Smale to create the general theory of dynamic systems".

[7] The couple collaborated in their work, jointly published "Structural Stability in the plane with enlarged boundary conditions" in 1959,[8] before Marília Chaves Peixoto's early death in 1961.