Iteration of meromorphic functions
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In this paper, the authors describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions, and some aspects where the transcendental case is analogous to the rational case are treated rather briefly here.Abstract:
This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental case is analogous to the rational case are treated rather briefly here. For example, we introduce the different types of components of the Fatou set that occur in the iteration of rational functions but omit a detailed description of these types. Instead, we concentrate on the types of components that are special to transcendental functions (Baker domains and wandering domains).read more
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Journal ArticleDOI
Holomorphic Dynamics By S. MOROSAWA, Y. NISHIMURA, M. TANIGUCHI and T. UEDA Cambridge Studies in Advanced Mathematics, 66. Cambridge University Press, 2000. ISBN 0 521 66258 3.
Journal ArticleDOI
Lambert's W function and convergence of infinite exponentials in the space of quaternions
TL;DR: In this article, the authors extended Lambert's W function in the space of quaternions and derived formulas for the left and right quaternion derivatives for f(z)=cz.
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Fatou and Julia like sets II.
TL;DR: In this article, a generalized escaping like set for a family of holomorphic functions on an arbitrary domain is introduced, and the connectedness of the Julia like set is also proved.
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On the set of limit functions in wandering domains
TL;DR: In this article, it was shown that the set of limit functions may consist of any given finite set of constant functions if the constant function ∞ belongs to this set, and that limit functions can only exist of a finite number of constants if this set is contained in the backward orbit of ∞ or if its elements form an irrationally indifferent cycle which is contained within the Julia set.
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Escaping points in the boundaries of Baker domains
TL;DR: In this paper, the authors studied the dynamical behaviour of points in the boundaries of simply connected invariant Baker domains of meromorphic maps with a finite degree on the domain and proved that if the boundary of the domain is of hyperbolic or simply parabolic type, then almost every point in the boundary with respect to harmonic measure escapes to infinity under iteration.
References
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TL;DR: In this paper, the authors present ideas and examples about the geometry of dynamics and bifurcations of ordinary differential equations, and demonstrate that the basic notion of stability and stability of vector fields can be easily explained for scalar autonomous equations.
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The Beauty of Fractals
TL;DR: A can is a can made of a steel sheet the surface of which is coated with a three-layered chromium coating, consisting of a metallic chromium coated, a crystalline chromium oxide coating and a non-crystalline hydrated chromiumoxide coating in this order.