Rotating an interval and a circle

Rotating an Interval and a Circle

We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the Black

Vanishing viscosity limit for incompressible flow inside a rotating circle

In this article we consider circularly symmetric incompressible viscous flow in a disk. The boundary condition is no-slip with respect to a 4 prescribed time-dependent rotation of the boundary about the center of the disk. We prove that, if the prescribed angular velocity of the boundary 5 has finite total variation, then the Navier–Stokes solutions converge strongly in L2 to the corresponding ...

Chain groups of homeomorphisms of the interval and the circle

We introduce and study the notion of a chain group of homeomorphisms of a one-manifold, which is a certain generalization of Thompson’s group F. Precisely, this is a group finitely generated by homeomorphisms, each supported on exactly one interval in a chain, and subject to a certain mild dynamical condition. The resulting class of groups exhibits a combination of uniformity and diversity. On ...

Unique Ergodicity of Circle and Interval Exchange Transformations with Flips

We study circle exchange transformations on three subintervals, that reverse orientation on at least one of the subintervals (a flip). We prove that if such a transformation has exactly one flip, then it has a periodic orbit and thus no dense orbit. For the cases of two and three flips, we construct uniquely ergodic minimal examples by finding a periodic point of an adapted Rauzy–Veech renormal...

A Connection Between Quadrature Formulas on the Unit Circle and the Interval