Hi!
Can somebody help me with the following problem. How to prove that map f(x)=asin(x) where a is constant is not structurally C^r stable for any r in N.
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.
Sign up to join this communityHi!
Can somebody help me with the following problem. How to prove that map f(x)=asin(x) where a is constant is not structurally C^r stable for any r in N.
Let $S$ be the set of points where $f' = 0$. Then $f(S)$ consists of just two points.
This property is preserved by any topological conjugacy, but it won't be true of a generic tiny perturbation of $f$.