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

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 $1\le d\le r\le\infty$ and $d<\infty$ and two different topologies on families. In particular, the case $d=r=1$ is new.