9 citations · 29 across the 14 of their papers we have counts for
15 papers
Normal forms in a neighborhood of hyperbolic periodic orbits for flows in dimension 3
Alena Erchenko, Kurt Vinhage, Yun Yang
In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of th…
Slow entropy and variational dynamical systems
Minhua Cheng, Carlos Ospina, Kurt Vinhage +1
We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entro…
The Zimmer Program for partially hyperbolic actions
Danijela Damjanovic, Ralf Spatzier, Kurt Vinhage +1
Zimmer's superrigidity theorems on higher rank Lie groups and their lattices launched a program of study aiming to classify actions of semisimple Lie groups and their lattices, kno…
Instability for rank one factors of product actions
Kurt Vinhage
We provide a counterexample to a standard interpretation of the Katok-Spatzier conjecture, and pose questions which may serve as reasonable replacements.
Slow entropy of higher rank abelian unipotent actions
Adam Kanigowski, Philipp Kunde, Kurt Vinhage +1
We study slow entropy invariants for abelian unipotent actions on any finite volume homogeneous space . For every such action we show that the topological slow entropy can…
Entropy rigidity for 3D conservative Anosov flows and dispersing billiards
Jacopo De Simoi, Martin Leguil, Kurt Vinhage +1
Given an integer , and a Anosov flow on some compact connected -manifold preserving a smooth volume, we show that the measure of maximal entropy (MME) is the…
Cartan Actions of Higher Rank Abelian Groups and their Classification
Ralf Spatzier, Kurt Vinhage
We study actions on arbitrary compact manifolds with a projectively dense set of Anosov elements and 1-dimensional coarse Lyapunov foliations.…
Horocycle flow on negative variable curvature surface is standard
Adam Kanigowski, Kurt Vinhage, Daren Wei
We provide a new proof that the horocycle flow preserving the Margulis measure on a variable negative curvature surface is standard. This was first proved by Ratner. The main purpo…
Kakutani Equivalence of Unipotent Flows
Adam Kanigowski, Kurt Vinhage, Daren Wei
We study Kakutani equivalence in the class of unipotent flows acting on finite volume quotients of semisimple Lie groups. For every such flow we compute the Kakutani invariant of M…
Entropy rigidity and flexibility for suspension flows over Anosov diffeomorphisms
Cameron Bishop, David Hughes, Kurt Vinhage +1
For any , area-preserving Anosov diffeomorphism of a surface, we show that a suspension flow over is -conjugate to a constant-time suspension flow of a…
Slow Entropy of Some Parabolic Flows
Adam Kanigowski, Kurt Vinhage, Daren Wei
We study nontrivial entropy invariants in the class of parabolic flows on homogeneous spaces, quasi-unipotent flows. We show that topological complexity (ie, slow entropy) can be c…
On the non-equivalence of the Bernoulli and K properties in dimension four
Adam Kanigowski, Federico Rodriguez-Hertz, Kurt Vinhage
We study skew products where the base is a hyperbolic automorphism of , the fiber is a smooth area preserving flow on with one fixed point (of high deg…
Cocycle rigidity of partially hyperbolic abelian actions with almost rank one factors
Kurt Vinhage
We extend the recent progress on the cocycle rigidity of partially hyperbolic homogeneous abelian actions to the setting with rank 1 factors in the universal cover. The method of p…
Local Rigidity of Higher Rank Homogeneous Abelian Actions: a Complete Solution via the Geometric Method
Kurt Vinhage, Zhenqi Jenny Wang
We show local and cocycle rigidity for partially hyperbolic translation actions on homogeneous spaces $\mc G/ Λ$. We consider a large class of actions whose geom…
On the Rigidity of Weyl Chamber Flows and Schur Multipliers as Topological Groups
Kurt Vinhage
We effectively conclude the local rigidity program for generic restrictions of partially hyperbolic Weyl chamber flows. Our methods replace and extend previous ones by circumventin…