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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A complementary proof of Baker's theorem of completely invariant components for transcendental entire functions
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TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
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Jack K. Hale,Hüseyin Koçak +1 more
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.