Presenter: George Haller

Spectral Submanifolds (SSMs) are special inertial manifolds that branch off from steady states (such fixed points, periodic orbits, traveling waves or toroidal attractors). A recent mathematical theory and computational platform for SSMs now enable the reduction of very high-dimensional dynamics to very low-dimensional attractors in dynamical systems. The resulting SSM-reduced models are explicit non-linear ODEs that can describe intrinsically nonlinear phenomena, such as transitions between steady states, bifurcations and chaotic behavior. I show applications of these results to fluids problems, including transitions in plane Couette and pipe flows. I also discuss briefly promising applications in soft robotics that point towards SSM-based flow control. Key references are (M. Cenedes et al., 2022), (G. Haller et al., 2023), (Kaszas and G. Haller, 2024), and (B. Kaszas et al., 2022).