Abstract:
We study the operators with dense , invariant and cyclic vector manifolds with the hypercyclicity and supercyclicity criteria. The structure of cycles and normal one¬-dimensional currents with rectifiable sets in metric and Banach spaces are shown. Equivalent norms for polynomials and equidis-tribution of the Fekete points on the sphere are determined. We stablish a weighted shift with cyclic square that, which is supercyclic and N¬-weakly hypercyclic and N¬¬¬¬¬-weakly supercyclic operators.We discuss the Schwartz-man cycles and ergodic solenoids and the decompostion of a cyclic normal currents metric space. We classify the Carleson measures and Logvinenko-¬Sereda sets and Beurling-¬Landau density on the compact manifolds.
