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arXiv · 1510.00723

Degree of recurrence of generic diffeomorphisms

Pierre-Antoine Guihéneuf
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Abstract

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.

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Pierre-Antoine Guihéneuf. 2019-02-27. Degree of recurrence of generic diffeomorphisms. https://doi.org/10.19086/da.7545

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