Moduli of 3-dimensional diffeomorphisms with saddle-foci

Abstract

We consider a space $\mathcal{U}$ of 3-dimensional diffeomorphisms $f$ with hyperbolic fixed points $p$ the stable and unstable manifolds of which have quadratic tangencies and satisfying some open conditions and such that $Df(p)$ has non-real expanding eigenvalues and a real contracting eigenvalue. The aim of this paper is to study moduli of diffeomorphisms in $\mathcal{U}$. We show that, for a generic element $f$ of $\mathcal{U}$, all the eigenvalues of $Df(p)$ are moduli and the restriction of a conjugacy homeomorphism to a local unstable manifold is a uniquely determined linear conformal map.