Dynamics and chaotic of polynomials on quasi banach spaces

Abstract EN

In the present paper, the concepts of a quasi-metric space, quasi-Banach space have been introduced.

We prove some facts which are defined on these spaces and define some polynomials on quasi-Banach spaces and studied their dynamics, such as, quasi cyclic and quasi hypercyclic.

We show the existence of quasi chaotic in the sense of Devaney (quasi D-chaotic) polynomials on quasi Banach space of qsummable sequences lq , 0

In general we also prove that P is quasi chaotic in the sense of Auslander and Yorke (quasi AY-chaotic) if and only if 0 belong to the Julia set of p, mN.

And then we prove that if the above polynomial P on lq , 0