Linearization of complex hyperbolic Dulac germs

Linearization of families of germs of hyperbolic vector fields

Holomorphic Motions, Fatou Linearization, and Quasiconformal Rigidity for Parabolic Germs

By applying holomorphic motions, we prove that a parabolic germ is quasiconformal rigid, that is, any two topologically conjugate parabolic germs are quasiconformally conjugate and the conjugacy can be chosen to be more and more near conformal as long as we consider these germs defined on smaller and smaller neighborhoods. Before to prove this theorem, we use the idea of holomorphic motions to ...

Minimal surfaces in germs of hyperbolic 3–manifolds

This article introduces a universal moduli space for the set whose archetypal element is a pair that consists of a metric and second fundamental form from a compact, oriented, positive genus minimal surface in some hyperbolic 3–manifold. This moduli space is a smooth, finite dimensional manifold with canonical maps to both the cotangent bundle of the Teichmüller space and the space of SO3(C) re...

Linearization: Geometric, Complex, and Conditional

Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various ...

Dulac and Gaudreault

This article is part of a larger research project on the different forms attraction has taken in the cultural series “animated pictures.” 2 Here we will focus our attention on the first signs of the paradigm which we propose to call cinématographie-attraction, a paradigm in which the question of “thresholds” seems to us to be essential. 3 Moving picture programs juxtaposed, one after the other,...