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Article Dans Une Revue Advances in Mathematics Année : 2024

Almost reducibility and oscillatory growth of Sobolev norms

Zhenguo Liang
  • Fonction : Auteur
Zhiyan Zhao
  • Fonction : Auteur
  • PersonId : 1067225
Qi Zhou
  • Fonction : Auteur

Résumé

For 1D quantum harmonic oscillator perturbed by a time quasi-periodic quadratic form of $(x,-{\rm i}\partial_x)$, we show its almost reducibility. The growth of Sobolev norms of solution is described based on the scheme of almost reducibility. By Anosov-Katok construction, we also show the existence of quasi-periodic quadratic perturbation for which the growth of ${\mathcal H}^s-$norm of the solution is $o(t^s)$ as $t\to\infty$ but arbitrarily "close" to $t^s$ in an oscillatory way.

Dates et versions

hal-03755122 , version 1 (21-08-2022)

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Zhenguo Liang, Zhiyan Zhao, Qi Zhou. Almost reducibility and oscillatory growth of Sobolev norms. Advances in Mathematics, 2024, 436, pp.109417. ⟨10.1016/j.aim.2023.109417⟩. ⟨hal-03755122⟩
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