Structural stability of attractor-repellor endomorphisms with singularities
arXiv:0809.0277
Abstract
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 is the disjoint union of a repulsive compact subset with a hyperbolic attractor on which 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.
37 pages