Sharp regularity of linearization for \(C^{1,1}\) hyperbolic diffeomorphisms (Q2439285)

This paper concerns the problem of \(C^{1,\beta}\) linearization of a hyperbolic \(C^{1,1}\) diffeomorphism \(F\) fixing the origin in a Banach space, i.e., the problem of existence of a \(C^{1,\beta}\) diffeomorphism \(\Phi\) such that \[ \Phi\circ F= DF(0)\circ\Phi \] on a neighbourhood of zero. An estimate of \(\beta\) is given and proved to be sharp in the planar case.