On a quartic polynomials family of two parameters. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Blé, G.; Castillo-Santos, F. E.; González, D.; Valdez, R.
• Is Part Of: Dynamical systems. Volume 36:Issue 1(2021)
• Page Start: 154
• Page End: 166
• Publication Date: 2021-01-02
• Subjects: Julia set -- quartic polynomials -- connectedness locus -- locally connected; Primary: 37F10 -- 37F45 -- 37F50; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2020.1849031
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: We consider a family of quartic polynomials generated by the composition of two quadratic polynomials. The elements of this family have two complex parameters, however they have at most two dynamic behaviors, since every map in this family have two critical points with the same forward orbits. In this paper, we study this quartic family in the complex parameter space, and we describe the dynamical plane for some special parameters. Moreover, we analyze the parameter space for these quartic polynomials with a super attracting fixed point. We describe the connectedness locus for this family, and we prove the locally connectedness of the boundary of hyperbolic components in the parameter space.