4 papers
Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning
Marius Willner, Marco Trenti, Dirk Lebiedz
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry unde…
Separatrix configurations in holomorphic flows
Nicolas Kainz, Dirk Lebiedz
We investigate properties of boundary orbits (separatrices) of canonical regions (basins/neighbourhoods of equilibria) in holomorphic flows with real-valued time. We establish the…
Sensitivities in complex-time flows: phase transitions, Hamiltonian structure and differential geometry
Dirk Lebiedz, Johannes Poppe
Reminiscent of physical phase transitions separatrices divide the phase space of dynamical systems with multiple equilibria into regions of distinct flow behavior and asymptotics.…
Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows
Nicolas Kainz, Dirk Lebiedz
In this follow-up paper, we investigate the global geometry and topology of dynamical systems with entire vector field , building on and constructively extendin…