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Preprint Aug 2026

Unstable Manifolds for the Kuramoto Model: Convergence to the Ott-Antonsen Manifold

In this paper, we study the finite-dimensional, homogeneous, all-to-all coupled Kuramoto model. We begin by performing a complete spectral analysis of all equilibria of the system. Motivated by this analysis, we then derive an explicit description of the unstable manifolds associated with the family of incoherent equil...

C. Kuehn, G. Landi · 0 citations
Preprint Sep 2026

Renormalized Invariant Manifolds

Invariant manifold theory for partial differential equations (PDEs) is technically challenging as we often lack spectral gaps. Motivated by recent progress using renormalization in various areas of mathematics, we introduce a spectral renormalization method for semilinear parabolic equations that creates an artificial...

C. Kuehn, Jan-Eric Sulzbach · 0 citations

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