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 c₀(Z) and c₀(N), respectively, and characterize hypercyclicity and supercyclicity of such kinds of shifts. Finally, we study hypercyclicity, supercyclicity of operators lI +μB, where I is identity and B is backward shift. We note that there are essential differences between the non-Archimedean and real cases.