Hyperbolic components in exponential parameter space
نویسندگان
چکیده
منابع مشابه
Hyperbolic Components in Exponential Parameter Space Composantes hyperboliques dans l’espace des applications exponentielles
We discuss the space of complex exponential maps Eκ: z 7→ e z +κ. We prove that every hyperbolic component W has connected boundary, and there is a conformal isomorphism ΦW :W → H − which extends to a homeomorphism of pairs ΦW : (W,W ) → (H − ,H−). This solves a conjecture of Baker and Rippon, and of Eremenko and Lyubich, in the affirmative. We also prove a second conjecture of Eremenko and Lyu...
متن کاملCombinatorics of Bifurcations in Exponential Parameter Space
We give a complete combinatorial description of the bifurcation structure in the space of exponential maps z 7→ exp(z) + κ. This combinatorial structure is the basis for a number of important results about exponential parameter space. These include the fact that every hyperbolic component has connected boundary [RS], a classification of escaping parameters [FRS], and the fact that all dynamic a...
متن کاملHyperbolic Space
Radial lines, suitably parameterized, are geodesics, but notice that the distance from the origin to the (Euclidean) unit sphere is infinite. This model makes it intuitively clear that the boundary at infinity of hyperbolic space is Sn−1. Hyperbolic space together with its boundary at infinity has the topology of a closed ball, and isometries of hyperbolic space extend uniquely to a homeomorphi...
متن کاملOnline State Space Model Parameter Estimation in Synchronous Machines
The purpose of this paper is to present a new approach based on the Least Squares Error method for estimating the unknown parameters of the nonlinear 3rd order synchronous generator model. The proposed method uses the mathematical relationships between the machine parameters and on-line input/output measurements to estimate the parameters of the nonlinear state space model. The field voltage is...
متن کاملUniversal Approximator Property of the Space of Hyperbolic Tangent Functions
In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2004
ISSN: 1631-073X
DOI: 10.1016/j.crma.2004.05.014