Fractals/exponential

right|thumb|parameter space of the complex exponential family f(z)=exp(z)+c. The parameter in the middle of the picture is postsingularly preperiodic (PSP). Eight parameter rays landing at this parameter are drawn in black. The bifurcation locus is grey, while hyperbolic components are shown as colored regions. In the theory of dynamical systems, the exponential map can be used as the evolution function of the discrete nonlinear dynamical system.Dynamics of exponential maps by Lasse Rempe Family The family of exponential functions is called the exponential family. Forms There are many forms of these maps,"Bifurcation Loci of Exponential Maps and Quadratic Polynomials: Local Connectivity, Triviality of Fibers, and Density of Hyperbolicity", Lasse Rempe, Dierk Schleicher many of which are equivalent under a coordinate transformation. For example two of the most common ones are: The second one can be mapped to the first using the fact that , so is the same under the transformation . The only difference is that, due to multi-valued properties of exponentiation, there may be a few select cases that can only be found in one version. Similar arguments can be made for many other formulas. How to compute it What is the continous iteration of ? "The function is one of the simpler applications of continuous iteration. The reason why is because regular iteration requires a fixed point in order to work, and this function has a very simple fixed point, namely zero: "Tetration FAQ by Henryk Trappman Andrew Robbins July 10, 2008 Images commons Category:Exponential maps Escaping set of (exp x-1)/2. (Arnaud Cheritat) See also Julia_and_Mandelbrot_sets_for_transcendental_functions by Gertbuschmann Exponential mapping of the plane Exponential maps THE EXPONENTIAL MAP IS CHAOTIC: AN INVITATION TO TRANSCENDENTAL DYNAMICS by ZHAIMING SHEN AND LASSE REMPE-GILLENDynamics of exponential maps by Lasse Rempewikipedia : Exponential map (discrete dynamical systems) Paper by N Fagella tetration fractals Paul Bourke fractals tetration Baker domains On the Stability of Julia Sets of Functions having Baker Domains by Arnd Lauber ( 2004)Approximation of Baker domains and convergence of Julia sets by Tania Garfias-Macedo aus Mexiko Stadt, Mexiko References