A study of a meromorphic perturbation of the sine family

• Autorzy: Domínguez Patricia , Vázquez Josué

Identyfikatory

DOI

10.1515/dema-2022-0002

• Języki publikacji: EN

Abstrakty

EN

We study the dynamics of a meromorphic perturbation of the family λsinz by adding a pole at zero and a parameter μ , that is, fλ,μ(z)=λsinz+μ/z , where λ,μ∈C⧹{0} . We study some geometrical properties of fλ,μ and prove that the imaginary axis is invariant under fn and belongs to the Julia set when ∣λ∣≥1 . We give a set of parameters (λ,μ) , such that the Fatou set of fλ,μ has two super-attracting domains. If λ=1 and μ∈(0,2) , the Fatou set of f1,μ has two attracting domains. Also, we give parameters λ,μ such that ±π/2 are fixed points of fλ,μ and the Fatou set of fλ,μ contains attracting domains, parabolic domains, and Siegel discs, we present examples of these domains. This paper closes with an example of fλ,μ , where the Fatou set contains two types of domains, for λ,μ given.

Słowa kluczowe

EN

iteration; fixed points; Fatou set; Julia set

PL

iteracja; punkt stały; zbiór Fatou; zbiór Julii

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 8--27
• Opis fizyczny: Bibliogr. 12 poz., rys., wykr.

Twórcy

autor

Domínguez Patricia

• Fac. Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, C.U., Puebla Pue, 72570, México

autor

Vázquez Josué

• Fac. Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Avenida San Claudio y 18 Sur, C.U., Puebla Pue, 72570, México

Bibliografia

• [1] I. N. Baker, J. Kotus, and L. Yinian, Iterates of meromorphic functions II: Examples of wandering domains, J. Lond. Math. Soc. 42 (1990), no. 2, 267–278.
• [2] I. N. Baker, J. Kotus, and L. Yinian, Iterates of meromorphic functions I, Ergodic Theory Dynam. Syst. 11 (1991), no. 2, 241–248.
• [3] I. N. Baker, J. Kotus, and L. Yinian, Iterates of meromorphic functions III: Preperiodic domains, Ergodic Theory Dynam. Syst. 11 (1991), no. 4, 603–618.
• [4] I. N. Baker, J. Kotus, and L. Yinian, Iterates of meromorphic functions IV: Critical finite functions, Results Math. 22 (1992), 651–656.
• [5] R. Devaney and L. Keen, Dynamics of tangent, Dynamical Systems (College Park, MD, 1986–87), Lecture Notes in Mathematics, vol. 1342, Springer, Berlin, 1988, pp. 105–111.
• [6] L. Keen and J. Kotus, Dynamics of the family lambda tan z, Conform. Geom. Dyn. 1 (1997), 28–57.
• [7] P. Domínguez and G. Sienra, A study of the dynamics of λ zsin , Int. J. Bifur. Chaos 12 (2002), no. 12, 2869–2883.
• [8] S. Zhang, On PZ type Siegel disk of the sine family, Ergodic Theory Dynam. Syst. 36 (2016), 973–1006.
• [9] P. Bhattacharya, Iteration of Analytic Functions, Ph.D. thesis, Imperial College London, 1969.
• [10] W. Bergweiler, An introduction to complex dynamics, Textos de Matemática, Universidad de Coimbra, Série B, 1995.
• [11] A. E. Eremenko and M. Y. Lyubich, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier 42 (1992), no. 4, 989–1020.
• [12] A. E. Eremenko and M. Y. Lyubich, The dynamics of analytic transformations, Leningrad Math. J. 1 (1990), no. 3, 563–634.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).