Good Lie Brackets for classical and quantum harmonic oscillators

Andrei Agrachev, Bettina Kazandjian, Eugenio Pozzoli

We study the small-time controllability problem on the Lie groups $S{L}_2(\mathbb{R})$ and $S{L}_2(\mathbb{R})⋉H_d(\mathbb{R})$ with Lie bracket methods (here $H_{d}(\mathbb{R…