Geodesic
Emergence and non-typicality of the finiteness of the attractors in many topologies
Informatics and Automation, Order and chaos in dynamical systems, Tome 297 (2017), pp. 7-37

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TRSPY_2017_297_a0,
     author = {Pierre Berger},
     title = {Emergence and non-typicality of the finiteness of the attractors in many topologies},
     journal = {Informatics and Automation},
     pages = {7--37},
     publisher = {mathdoc},
     volume = {297},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a0/}
}
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Pierre Berger. Emergence and non-typicality of the finiteness of the attractors in many topologies. Informatics and Automation, Order and chaos in dynamical systems, Tome 297 (2017), pp. 7-37. http://geodesic.mathdoc.fr/item/TRSPY_2017_297_a0/