Iterates of Meromorphic Functions II: Examples of Wandering Domains

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

doi:10.1112/jlms/s2-42.2.267

Cited by 49 publications

(51 citation statements)

References 7 publications

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“…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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“…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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“…We prove there that the packing measure is locally infinite on J r (F λ ) whereas the Hausdorff measure is on J r (F λ ) finite and positive. We also show that the Hausdorff dimension of J r (F λ ) is in the open interval (1,2). All these geometric properties of the set J r (F λ ) clearly indicate that this is the right object to deal with.…”

Section: Introductionmentioning

confidence: 87%

Geometry and dynamics of some meromorphic functions

Kotus¹,

Urbański²

2006

Mathematische Nachrichten

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Themeromorphic maps fλ (z) = λ (1 – exp(–2z))–1, λ > 0, of the complex plane are thoroughly investigated. With each map fλ associated is its projection Fλ on the infinite cylinder Q. This map and the set Jr (Fλ) consisting of those points in the cylinder Q whose ω ‐limit set under Fλ is not contained in the set {0, –∞} will form the primary objects of our interest in this article. Let hλ = HD(Jr (Fλ)) be the Hausdorff dimension of Jr (Fλ). We prove that hλ ∈ (1, 2). The hλ ‐dimensional Hausdorff measure Hhλ of Jr (Fλ) is proven to be positive and finite. The hλ ‐dimensional packing measure of Jr (Fλ) is shown to be locally infinite at every point of this set. There exists a unique Borel probability Fλ ‐invariant measure μλ on Jr (Fλ) absolutely continuous with respect to the Hausdorff measure Hhλ. This measure turns out to be ergodic and equivalent to Hhλ. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…Since g(F(G)) C F(G), each g G G omits J(G) on V = U\{0} which implies every element in G is normal on U, which gives a contradiction. D We denote the solutions by {a n }, that is, f{a n ) = wo and f'(a n ) / 0 for n 6 N. If h is transcendental, we have Q(otj,h) < 1/2 for some ai,a 2 ,a 3 .…”

Section: J(g) = (J J(g)mentioning

confidence: 99%

“…The development of complex dynamics took nearly a century, from the work of Fatou [7,8] and Julia [12,13] appearing in [1918][1919][1920][1921][1922] to the recent studies on the dynamics of transcendental meromorphic functions [2,3,4]. Nowadays, complex dynamics has a new significant development with the explosion of popular interest in the beautiful fractal objects that form the subject matter of the theory.…”

Section: Introductionmentioning

confidence: 99%