2023/03/01 by Pietro Baldi, Filippo Giuliani, Baldi, Pietro +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35A24 #35B34 #37D45 #74H65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2303.00688
openalex publication_date 2023/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity is encoded in the time between oscillations of the norm, which can be chosen in any prescribed way. This phenomenon, that we name as effective chaos (it occurs over a long, but finite, time scale), is consequence of the existence of symbolic dynamics for an effective system. Since the first order resonant dynamics has been proved to be essentially stable, we need to perform a second order analysis to find an effective model displaying chaotic dynamics. More precisely, after some reductions, this model behaves as two weakly coupled pendulums.