The classical Takens delay-embedding theorem from 1981 asserts that for a generic pair of a smooth diffeomorphism $T$ on a compact manifold $M$ of dimension $k$ and a smooth real observable $h$ on $M$, the $(2k+1)$-delay coordinate map defined by $T$ and $h$ is a smooth embedding of the dynamical system $(M, T)$ into $R^{2k+1}$. The result was generalized by many authors in various contexts.

We present a probabilistic version of the Takens delay-embedding theorem for Lipschitz maps on a Borel set $X$, which enables to reduce the number of required delay coordinates to any $k$ larger than the Hausdorff dimension of $X$. We also provide a non-dynamical probabilistic embedding theorem of similar type, which strengthens a previous result by Alberti, Bolcskei, De Lellis, Koliander and Riegler.

This a joint work with Yonatan Gutman (IMPAN) and Adam Śpiewak (Bar Ilan University).

Meeting ID: 852 4277 3200 Passcode: 103121