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On a quartic polynomials family of two parameters
Dynamical Systems ( IF 0.5 ) Pub Date : 2020-12-06 , DOI: 10.1080/14689367.2020.1849031
G. Blé 1 , F. E. Castillo-Santos 1 , D. González 1 , R. Valdez 2
Affiliation  

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.



中文翻译:

关于两个参数的四次多项式族

摘要

我们考虑由两个二次多项式组成的四次多项式族。该族的元素具有两个复杂的参数,但是它们最多具有两个动态行为,因为该族中的每个地图都有两个具有相同前向轨道的临界点。在本文中,我们研究了复参数空间中的四次族,并描述了一些特殊参数的动力学平面。此外,我们分析了具有超吸引不动点的这些四次多项式的参数空间。我们描述了该族的连通性轨迹,并证明了参数空间中双曲分量边界的局部连通性。

更新日期:2020-12-06
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