R. de la Llave

Existence and Regularity of Stable Resonant Spectral Submanifolds and Linearization Maps

We prove the existence of $C^{r,1-}$-regular stable invariant manifolds and linear conjugacies for analytic maps near a hyperbolic fixed point in the presence of resonances. The regularity exponent $r$ depends on the minimal resonant index, while the H\"older exponent can be chosen arbitrarily close to $1$, i.e., $1-\v...