On the sharpness of the $C^1$-norm threshold for perturbations in the normally hyperbolic invariant manifold theorem---a toy model perspective

Yujie Huang, Junhao Li, Lin Wang

The classical normally hyperbolic invariant manifold theorem asserts that a \(C^1\) normally hyperbolic invariant manifold persists under \(C^1\) small perturbations. For a family…