Iterates of Meromorphic Functions IV: Critically Finite Functions

Baker, I. N.; Kotus, Janina; Yinian, Lü

doi:10.1007/bf03323112

Cited by 92 publications

(96 citation statements)

References 12 publications

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“…In this section we shall prove that no function in the family F can have a Herman ring. In [11] and in [5] it is proved that maps in F have no wandering domains. The stable behavior for functions in F is therefore either eventually attractive, parabolic, or lands on a cycle of Siegel disks.…”

Section: The Dynamic Plane: the Fatou Set F λmentioning

confidence: 99%

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Dynamics of the family 𝜆tan𝑧

Keen

Kotus

1997

Conform. Geom. Dyn.

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Section: The Dynamic Plane: the Fatou Set F λmentioning

confidence: 99%

“…The dynamical properties of the tangent family were first studied by Devaney and Keen in [10,11] and pursued by Baker, Kotus, and Lü in [2,3,4,5]. W.H.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the family 𝜆tan𝑧

Keen

Kotus

1997

Conform. Geom. Dyn.

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“…Periodic components of the Fatou set of elliptic functions may be attracting domains, parabolic domains, Siegel disks, or Herman rings. In particular, elliptic functions have no wandering domains or Baker domains [1,12,22].…”

Section: Background On the Dynamics Of Meromorphic Functionsmentioning

confidence: 99%

A fundamental dichotomy for Julia sets of a family of elliptic functions

Koss

2009

Proc. Amer. Math. Soc.

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Abstract. We investigate topological properties of Julia sets of iterated elliptic functions of the form g = 1/℘, where ℘ is the Weierstrass elliptic function, on triangular lattices. These functions can be parametrized by C − {0}, and they all have a superattracting fixed point at zero and three other distinct critical values. We prove that the Julia set of g is either Cantor or connected, and we obtain examples of each type.

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“…Let S be the class of critically finite transcendental meromorphic function f (z). Baker [2] proved the following: Theorem 1.1. Let f ∈ S. Then, f (z) has no wandering domains.…”

Section: Introductionmentioning

confidence: 96%

“…The initial study of iterations of transcendental meromorphic functions is mainly found in [1,2,3,5]. Further, researches in this direction are pursued in [7,13,18,26].…”

Section: Introductionmentioning

confidence: 99%

Chaos in dynamics of a family of transcendental meromorphic functions

Sajid¹,

Kapoor²

2017

Journal of Nonlinear Analysis and Application

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In this paper, the chaotic behaviours in the real and complex dynamics of ζ λ (z) = λ z z+1 e −z , λ > 0, z ∈ C are investigated. The bifurcation in the dynamics of ζ λ (x), x ∈ R \ {−1}, occurs at several parameter values and the dynamics becomes chaotic when the parameter λ crosses certain values. The Lyapunov exponent of ζ λ (x) is computed for quantifying the chaos. The characterization of the Julia set of ζ λ (z) as complement of the basin of attraction is found and is applied to computationally simulate the images of the Julia sets. Finally, the results on the dynamics of ζ λ (z) are compared with the known results.

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Iterates of Meromorphic Functions IV: Critically Finite Functions

Cited by 92 publications

References 12 publications

Dynamics of the family 𝜆tan𝑧

Dynamics of the family 𝜆tan𝑧

A fundamental dichotomy for Julia sets of a family of elliptic functions

Chaos in dynamics of a family of transcendental meromorphic functions

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