关于两个参数的四次多项式族

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2020-12-06 DOI:10.1080/14689367.2020.1849031

G. Blé, F. E. Castillo-Santos, D. González, R. Valdez

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引用次数: 2

摘要

摘要我们考虑由两个二次多项式组成的一组四次多项式。这个族的元素有两个复杂的参数，但它们最多有两个动力学行为，因为这个族中的每个地图都有两个具有相同前向轨道的临界点。本文在复参数空间中研究了这个四次族，并描述了一些特殊参数的动力平面。此外，我们还分析了这些具有超吸引不动点的四次多项式的参数空间。我们描述了这个族的连通性轨迹，并证明了参数空间中双曲分量边界的局部连通性。

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On a quartic polynomials family of two parameters

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.

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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences