ESCAPING POINTS OF EXPONENTIAL MAPS
نویسندگان
چکیده
منابع مشابه
Connected Escaping Sets of Exponential Maps
We show that, for many parameters a ∈ C, the set I(fa) of points that converge to infinity under iteration of the exponential map fa(z) = e + a is connected. This includes all parameters for which the singular value a escapes to infinity under iteration of fa.
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 کاملTopological 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 کاملJa n 20 07 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 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: Journal of the London Mathematical Society
سال: 2003
ISSN: 0024-6107,1469-7750
DOI: 10.1112/s0024610702003897