2008/09/01 by Berger, Pierre
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.0809.0277
We prove a theorem on structural stability of smooth attractor-repellor endomorphisms of compact manifolds, with singularities. By attractor-repellor, we mean that the non-wandering set of the dynamics f is the disjoint union of a repulsive compact subset with a hyperbolic attractor on which f acts bijectively. The statement of this result is both infinitesimal and dynamical. Up to our knowledge, this is the first in this hybrid direction. Our results generalize also a Mather's theorem in singularity theory which states that infinitesimal stability implies structural stability for composed mappings, to the larger category of laminations.