2 citations · 2 across the 6 of their papers we have counts for
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A note on cocycles in
Nikolaos Karaliolios
This short note studies -smooth cocycles in that have degree and are non-homotopic to constants. The study picks up from where the author's…
Furstenberg counterexamples over Diophantine rotations
Nikolaos Karaliolios
We construct cocycles in over Diophantine rotations that are minimal and not uniquely ergodic. Such cocycles are dense in an open subset of cocycles over…
Anosov-Katok constructions for quasi-periodic cocycles
Nikolaos Karaliolios, Xu Xu, Qi Zhou
We prove that if the frequency of the quasi-periodic cocycle is Diophantine, then the following properties are dense in the subcritical regime: for any $\frac{1…
Fibered rotation vector and hypoellipticity for quasiperiodic cocycles in compact Lie groups
Nikolaos Karaliolios
Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi-periodic cocycles in , a compact Lie g…