This is a somewhat philosophical talk (without theorems) about the notion of an elementary piece of dynamics and its generation. The emphasis will put on constructions. The works of Newhouse in the 70's stated that the locally generic coexistence of infinitely many sinks at (dissipative) homoclinic tangencies. We first study how this question can be adapted to heterodimensional cycles in partially hyperbolic settings (where sinks/sources cannot be displayed). While sinks are clearly independent pieces of dynamics, the first step is to discuss "what is (or what should be) an independent piece of dynamics" (with an special emphasis in the partially hyperbolic context). We propose that homoclinic classes play such a role. Thereafter we will explain Newhouse's construction of diffeomorphisms with infinitely many sinks. This follows the inductive pattern: a tangency leads to a sink and a new tangency. We will see that this sort of inductive construction cannot lead to "infinitely many independent homoclinic classes" and explain the obstructions.
Meeting ID: 852 4277 3200 Passcode: 103121