Research Of N Multiple-Nonwandering Operator And Its Properties

The paper takes the method of differential dynamics and basic theories of theoperator as tools on the basis of Hypercyclicity of operator, Chaos, do further researchto the nonwandering property of the operators. Especially, this paper based on thedefinition of nonwandering operator in Banach space, we give the definition of nmultiple-nonwandering operators and show that every infinite dimensional seperableBanach space with an unconditional basis supports a n multiple-nonwanderingoperator by the methods of eigenvectors. Moreever, we give some good properties ofn multiple-nonwandering operator.On the other hand, we make certain study to the n multiple-nonwandring ofComposition operators. we prove C_? is a n multiple-nonwandering operator when(?) is hyperbolic holomorphic map on H² space, when is the best place to study theinteraction between the theories of linear operators and analytic functions.Furthermore, we prove C_? is n multiple-nonwandering on H^p and B^p when (?) ishyperbolic.Next, this paper studies weighted shifts operator (bilateral weighted forward orunilateral weighted backward) on sequence space l^p(1≤p<∞) and characterizestheir n multiple-nonwandering property when their weighting sequences satisfycertain condition.In the end, we extend the study of spectra decomposition of nonwanderingoperator , give the spectra decomposition of n multiple-nonwandering operator andthe provement. Moreover ,the paper also studies the local structural stability of nmultiple-nonwandering operators by the methord of nonwandering operator.