Geodesic
Degree of recurrence of generic diffeomorphisms
Discrete analysis (2019) Cet article a éte moissonné depuis la source Scholastica

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We study spatial discretizations of dynamical systems: is it possible to recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of orbits with a fixed number of digits. We show that for every $r\ge 1$, the dynamics of the discretizations of a $C^r$ generic conservative diffeomorphism of the torus is very different from that observed in the $C^0$ regularity. The proof of our results involves in particular a local-global formula for discretizations, as well as a study of the corresponding linear case, which uses ideas from the theory of quasicrystals.
Publié le : 
@article{DAS_2019_a19,
     author = {Pierre-Antoine Guih\'eneuf},
     title = {Degree of recurrence of generic diffeomorphisms},
     journal = {Discrete analysis},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2019_a19/}
}
TY  - JOUR
AU  - Pierre-Antoine Guihéneuf
TI  - Degree of recurrence of generic diffeomorphisms
JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a19/
LA  - en
ID  - DAS_2019_a19
ER  - 
%0 Journal Article
%A Pierre-Antoine Guihéneuf
%T Degree of recurrence of generic diffeomorphisms
%J Discrete analysis
%D 2019
%U http://geodesic.mathdoc.fr/item/DAS_2019_a19/
%G en
%F DAS_2019_a19
Pierre-Antoine Guihéneuf. Degree of recurrence of generic diffeomorphisms. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a19/