Exploring Singularities in point clouds with the graph Laplacian: An explicit approach

no code implementations • 31 Dec 2022 • Martin Andersson, Benny Avelin

We develop theory and methods that use the graph Laplacian to analyze the geometry of the underlying manifold of point clouds.

Historic behaviour vs. physical measures for irrational flows with multiple stopping points

no code implementations • 18 Oct 2020 • Martin Andersson, Pierre-Antoine Guihéneuf

We study Birkhoff averages along trajectories of smooth reparameterizations of irrational linear flows of the two torus with two stopping points, say $\mathbf p$ and $\mathbf q$, of quadratic order.

Dynamical Systems 37C10, 37C40 (primary), and 11K50, 11J71 (secondary)