Dynamical system f(x)=(x^4)sin(1/x). How to determine the stabilityWatch
I found the equilibrium points x=0 and x=1/(kπ), where k is integer. .
When k is 'even',
which is positive, therefore not asymptotically stable.
And when k is 'odd',
which is negative, therefore asymptotically stable.
But f′(x=0)=0, which is not hyperbolic. And this is the part that I can not solve.
Thanks in advance.