This paper is based on the author’s previous work [S4]. We consider fiber-preserving complex dynamics on fiber bundles whose fibers are Riemann spheres and whose base spaces are compact metric spaces. In this context, without any assumption on (semi-)hyperbolicity, we show that the fiberwise Julia sets are uniformly perfect. From this result, we show that, for any semigroup G generated by a com...

This paper is based on the author’s previous work [S4]. We consider fiber-preserving complex dynamics on fiber bundles whose fibers are Riemann spheres and whose base spaces are compact metric spaces. In this context, without any assumption on (semi-)hyperbolicity, we show that the fiberwise Julia sets are uniformly perfect. From this result, we show that, for any semigroup G generated by a com...

The Hölder continuity of the truncated moment map a shade function in Euclidean space is established vicinity principal semi-algebraic set. proof combines volume bounds sets and convex optimization methods. main estimate applied to potential type transform specific two real variables, for perturbations quadrature domains.

Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. In this paper, we present a procedure based on computing critical points some well-chosen function that guarantees computation in each bounded connected component (real) atomic set. Our technique is intuitive principal, performs well previously difficult examples, ...

Computing control invariant sets is paramount in many applications. The families of commonly used for computations are ellipsoids and polyhedra. However, searching a set over the family conservative systems more complex than unconstrained linear time systems. Moreover, even if may be approximated arbitrarily closely by polyhedra, complexity polyhedra grow rapidly certain directions. An attracti...