Decay of geometry for Fibonacci critical covering maps of the circle
Derivatives of circle rotations, and similarity of orbits.
Differentiable rigidity and smooth conjugacy.
Diophantine classes, dimension and Denjoy maps
Dispersion properties of ergodic translations.
Dynamically defined Cantor sets under the conditions of McDuff's conjecture
We prove that if the Cantor set K, dynamically defined by a function , satisfies the conditions of McDuff’s conjecture then it cannot be C¹-minimal.
Dynamics of circle maps with flat spots
We study a certain class of weakly order preserving, non-invertible circle maps with irrational rotation numbers and exactly one flat interval. For this class of circle maps we explain the geometric and dynamic structure of orbits. In particular, we formulate the so called upper and lower scaling rules which show an asymmetric and double exponential decay of geometry.