We investigate the dynamics of semigroups generated by polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. Moreover, we investigate the associated random dynamics of polynomials. Furthermore, we investigate the fiberwise dynamics of skew products related to polynomial semigroups with bounded planar postcritical set. Using uniform fiberwise quasi...

Acceleration profile generation for jerk limitation is a major issue in automated industrial applications like computer numerical control (CNC) machinery and robotics. The automation machinery dynamics should be kept as smooth as possible with suitable controllers where trajectory precision ensures quality while smoothness decreases machinery stress. During the operation of commercially availab...

We introduce a class of dynamical systems of algebraic origin, consisting of selfinteracting irreducible polynomials over a field. A polynomial f is made to act on a polynomial g by mapping the roots of g. This action identifies a new polynomial h, as the minimal polynomial of the displaced roots. By allowing several polynomials to act on one another, we obtain a self-interacting system with a ...

Providing smooth reference trajectories can effectively increase performance and accuracy of tracking control applications while overshoot unwanted vibrations are reduced. Trajectory planning computations often be simplified significantly by transforming the system dynamics into decoupled integrator chains using methods such as feedback linearization, differential flatness or Brunovsky normal f...

We show that the mixing time of Glauber (single edge update) dynamics for the random cluster model at q = 2 is bounded by a polynomial in the size of the underlying graph. As a consequence, the Swendsen-Wang algorithm for the ferromagnetic Ising model at any temperature has the same polynomial mixing time bound.

In this paper we prove that a polynomial system can be always mapped by some rational mapping into a general quadratic system. This result is useful for studies of systems with a complex dynamics. One generalization is discussed. Our approach is based on theorems on algebraic dependent polynomials. Key-Words:Polynomial, polynomial system, quadratic system, rational mapping, algebraic dependence...