In some applications not only the knowledge of the behaviour of trajectories of a map is important, but also their displacements. We describe in detail the distribution of elements of the displacement sequence along a trajectory of an orientation preserving circle homeomorphism ϕ with irrational rotation number ϱ(ϕ). The values of displacement are dense in a set which depends on the map γ (semi-)conjugating ϕ with the rotation...

We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as boundedness, superficiality, local discrete radius of curvature are linked with dynamical properties of the circle homeomorphism which generates them: rotation number and its continued fraction...

In this paper is described a methodology of design of satellite mechanism consisting of two noncircular gears (externally toothed rotor and internally toothed curvature) and circular gears (satellites). In the presented methodology is assumed that the rotor pitch line is known, and the curvature pitch line is necessary to designate. The presented methodology applies to mechanisms for which the number of the curvature humps is at...