11 citations · 18 across the 2 of their papers we have counts for
6 papers
The Lorenz Renormalization Conjecture
Björn Winckler
The renormalization paradigm for low-dimensional dynamical systems is that of hyperbolic horseshoe dynamics. Does this paradigm survive a transition to more physically relevant sys…
The Rigidity Conjecture
Marco Martens, Liviana Palmisano, Björn Winckler
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many cla…
Instability of Renormalization
Marco Martens, Björn Winckler
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization…
On the Hyperbolicity of Lorenz Renormalization
Marco Martens, Björn Winckler
We consider infinitely renormalizable Lorenz maps with real critical exponent and combinatorial type which is monotone and satisfies a long return condition. For these combin…
Existence of a Lorenz renormalization fixed point of an arbitrary critical order
Denis Gaidashev, Bjorn Winckler
We present a proof of the existence of a renormalization fixed point for Lorenz maps of the simplest non-unimodal combinatorial type ({0,1},{1,0,0}), and with a critical point of a…
A renormalization fixed point for Lorenz maps
Björn Winckler
A Lorenz map is a Poincaré map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of…