21 citations · 47 across the 6 of their papers we have counts for
6 papers
Global Dynamics, Blow-Up, and Bianchi Cosmology
Nitsan Ben-Gal, Bernhard Brehm, Johannes Buchner +8
Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equation…
Connected components of meanders: I. Bi-rainbow meanders
Anna Karnauhova, Stefan Liebscher
Closed meanders are planar configurations of one or several disjoint closed Jordan curves intersecting a given line or curve transversely. They arise as shooting curves of paraboli…
Oscillatory singularities in Bianchi models with magnetic fields
Stefan Liebscher, Alan D. Rendall, Sophonie Blaise Tchapnda
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approxima…
Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
Stefan Liebscher
We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant…
Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles
Stefan Liebscher, Jörg Härterich, Kevin Webster +1
We consider cosmological models of Bianchi type. In particular, we are interested in the alpha-limit dynamics near the Kasner circle of equilibria for Bianchi classes VIII and IX.…
Bifurcations without parameters: some ODE and PDE examples
Bernold Fiedler, Stefan Liebscher
Standard bifurcation theory is concerned with families of vector fields , , involving one or several constant real parameters . Viewed as a different…