
S. Newhouse, J. Palis, and F. Takens have recently proved the global structural stability of a one parameter unfolding of a saddle node when the nonwandering set is finite and transversality conditions are satisfied. (The diffeomorphism is Morse-Smale except for the saddle node.) Using their local unfolding of a saddle node and our method of compatible families of unstable disks (instead of the more restrictive method of compatible systems of unstable tubular families), we are able to extend one of their results to the case where the nonwandering set is infinite. We assume that a saddle node is introduced away from the rest of the nonwandering set which is hyperbolic (Axiom A), and that a (strong) transversality condition is satisfied.
Structural stability and analogous concepts of solutions to ordinary differential equations, Strong Transversality Condition, Families of Diffeomorphisms, Saddle Node P, Dynamical systems with hyperbolic behavior, Attractors and repellers of smooth dynamical systems and their topological structure, Hyperbolic Structure, Nonwandering Set, Stability theory for smooth dynamical systems, Structural Stability
Structural stability and analogous concepts of solutions to ordinary differential equations, Strong Transversality Condition, Families of Diffeomorphisms, Saddle Node P, Dynamical systems with hyperbolic behavior, Attractors and repellers of smooth dynamical systems and their topological structure, Hyperbolic Structure, Nonwandering Set, Stability theory for smooth dynamical systems, Structural Stability
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