Dynamics and Chaotic of Polynomials on Quasi Banach Spaces - Jasim Al-Jawari, Naseif; Nazar Mustafa, Arwa (Iraqi Journal of Science, 2023)
In the present paper, the concepts of a quasi-metric space, quasi-Banach spacehave been introduced. We prove some facts which are defined on these spaces anddefine some polynomials on quasi-Banach spaces and studied their dynamics, suchas, quasi cyclic and quasi hypercyclic. We show the existence of quasi chaotic in thesense of Devaney (quasi D-chaotic) polynomials on quasi Banach space of qsummablesequences lq , 0<q<1 such polynomials P is defined by P((xi)i)=(p(xi+m))iwhere p:CC, p(0) = 0. In general we also prove that P is quasi chaotic in the senseof Auslander and Yorke (quasi AY-chaotic) if and only if 0 belong to the Julia set ofp, mN. And then we prove that if the above polynomial P on lq , 0<q<1 is quasiAY-chaotic then so is P where R+ with 1 and Pn for each n2.