We investigate the dynamics of polynomial semigroups (semigroups generated by a family of polynomial maps on the Riemann sphere Ĉ) and the random dynamics of polynomials on the Riemann sphere. Combining the dynamics of semigroups and the fiberwise (random) dynamics, we give a classification of polynomial semigroups G such that G is generated by a compact family Γ, the planar postcritical set of...

in this paper, trajectory generation for the 4 dof arm of surena iii humanoid robot with the purpose of optimizing energy and avoiding a moving obstacle is presented. for this purpose, first, kinematic equations for a seven dof manipulator are derived. then, using the lagrange method, an explicit dynamics model for the arm is developed. in the next step, in order to generate the desired traject...

Using techinques of complex dynamics we prove the conjecture of Sheil-Small and Wilmshurst that the harmonic polynomial z − p(z), deg p = n > 1, has at most 3n− 2 complex zeros.

This paper, motivated from complex dynamics and algebraic geometry, studies the moduli space of polynomial maps of C, from the standpoint of their fixed-point eigenvalues. We denote by e Pd the set of affine conjugacy classes of f(z) ∈ C[z] with degC = d, and define the map Φd : e Pd → e Λd := n (λ1, . . . , λd) ∈ C d ̨

Motivated by the ‘subgraphs world’ view of the ferromagnetic Ising model, we analyse the mixing times of Glauber dynamics based on subset expansion expressions for classes of graph, hypergraph and matroid polynomials. With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs, hypergraphs and matroids of bounded tree-width. This extends...