What is ... a blender?
What is a blender? In six illustrated pages we define the construction of a blender and the role it plays in the study of smooth dynamical systems.
math.DS↗
arXiv subjects
Lorenzo Diaz
Publications and source records attributed to Lorenzo Diaz.
Collision, explosion and collapse of homoclinic classes
Homoclinic classes of generic $C^1$-diffeomorphisms are maximal transitive sets and pairwise disjoint. We here present a model explaining how two different homoclinic classes may intersect, failing to be disjoint. For that we construct a one-parameter family of diffeomorphisms $(g_s)_{s\in [-1,1]}$ with hyperbolic points $P$ and $Q$ having nontrivial homoclinic classes, such that, for $s>0$, the classes of $P$ and $Q$ are disjoint, for $s<0$, they are equal, and, for $s=0$, their intersection is a saddle-node.
math.DS↗