Dynamics of linear operators on non-Archimedean vector spaces

In the present paper we study dynamics of linear operators defined on topological vector space over non-Archimedean valued fields. We give sufficient and necessary conditions of hypercyclicity (resp. supercyclicity) of linear operators on separable F-spaces. It is proven that a linear operator T on topological vector space X is hypercyclic (supercyclic) if it satisfies Hypercyclicity (resp. Supercyclicity) Criterion. We consider backward shifts on c(0)(Z) and c(0)(N), respectively, and characterize hypercyclicity and supercyclicity of such kinds of shifts. Finally, we study hypercyclicity, supercyclicity of operators lambda I + mu B, where I is identity and B is backward shift. We note that there are essential differences between the non-Archimedean and real cases.