Ja n 20 07 CLASSIFICATION OF ESCAPING EXPONENTIAL MAPS
نویسنده
چکیده
We give a complete classification of the set of parameters κ for which the singular value of Eκ : z 7→ exp(z) + κ escapes to ∞ under iteration. In particular, we show that every path-connected component of this set is a curve to infinity.
منابع مشابه
Topological Dynamics of Exponential Maps on Their Escaping Sets
For the family of exponential maps Eκ(z) = exp(z)+κ, we prove an analog of Böttcher’s theorem by showing that any two exponential maps Eκ1 and Eκ2 are conjugate on suitable subsets of their escaping sets, and this conjugacy is quasiconformal. Furthermore, we prove that any two attracting and parabolic exponential maps are conjugate on their sets of escaping points; in fact, we construct an anal...
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 کاملM ar 2 00 7 CLASSIFICATION OF ESCAPING EXPONENTIAL MAPS
We give a complete classification of the set of parameters κ for which the singular value of Eκ : z 7→ exp(z) + κ escapes to ∞ under iteration. In particular, we show that every path-connected component of this set is a curve to infinity.
متن کاملA pr 2 00 5 CLASSIFICATION OF ESCAPING EXPONENTIAL MAPS
We give a complete classification of the set of parameters κ for which the singular value of Eκ : z 7→ exp(z) + κ escapes to ∞ under iteration. In particular, we show that every path-connected component of this set is a curve to infinity.
متن کاملJa n 20 09 PHYSICAL MEASURES FOR INFINITE - MODAL MAPS
Abstract. We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover we show that both the densities of these measures and their entropy vary continuously with t...
متن کامل