Structural stability theorem

Let M be a compact differentiable manifold and let f:MM be a Cr diffeomorphism.

Then, f is structurally stable in the C1 topologyPlanetmathPlanetmath if and only if it is Axiom A and satisfies the strong transversality condition. The question of knowing if this is valid for the Cr topology, r2 is still open.

Title Structural stability theorem
Canonical name StructuralStabilityTheorem
Date of creation 2014-03-19 22:14:32
Last modified on 2014-03-19 22:14:32
Owner Filipe (28191)
Last modified by Filipe (28191)
Numerical id 5
Author Filipe (28191)
Entry type Theorem
Synonym stability conjecture
Related topic Ω-stability theorem