Emergence and non-typicality of the finiteness of the attractors in many topologies

详细

We introduce the notion of emergence for a dynamical system and conjecture the local typicality of super complex ones. Then, as part of this program, we provide sufficient conditions for an open set of C^d-families of C^r-dynamics to contain a Baire generic set formed by families displaying infinitely many sinks at every parameter, for all 1 ≤ d ≤ r ≤ ∞ and d < ∞ and two different topologies on families. In particular, the case d = r = 1 is new.