Linéarisation des perturbations holomorphes des rotations et applications
Compacts connexes invariants par une application univalente
Let K be a compact connected subset of cc, not reduced to a point, and F a univalent map in a neighborhood of K such that F(K) = K. This work presents a study and a classification of the dynamics of F in a neighborhood of K. When ℂ K has one or two connected components, it is proved that there is a natural rotation number associated with the dynamics. If this rotation number is irrational, the situation is close to that of “degenerate Siegel disks” or “degenerate Herman rings” studied by R. Pérez-Marco...
Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure
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