Which sequences are orbits?

被引：0

作者：

Daniel A. Nicks

David J. Sixsmith

机构：

[1] University of Nottingham,School of Mathematical Sciences

[2] The Open University,School of Mathematics and Statistics

来源：

Analysis and Mathematical Physics | 2021年 / 11卷

关键词：

Iteration; Orbits; Holomorphic dynamics; Quasiregular dynamics; Primary 37F10; Secondary 30D05; 30C62;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study. In particular, restricting to the complex plane, we start with a sequence of complex numbers and study the functions (if any) for which this sequence is an orbit under iteration. This gives rise to questions of existence and of uniqueness. We resolve some questions, and show that these issues can be quite delicate.

引用

共 8 条

[1] Fletcher AN(2016)Superattracting fixed points of quasiregular mappings Ergod. Theory Dyn. Syst. 36 781-793
[2] Nicks DA(1998)On local injectivity and asymptotic linearity of quasiregular mappings Stud. Math. 128 243-271
[3] Gutlyanskiĭ VY(2016)On the set where the iterates of an entire function are neither escaping nor bounded Ann. Acad. Sci. Fenn. Math. 41 561-578
[4] Martio O(undefined)undefined undefined undefined undefined-undefined
[5] Ryazanov VI(undefined)undefined undefined undefined undefined-undefined
[6] Vuorinen M(undefined)undefined undefined undefined undefined-undefined
[7] Osborne JW(undefined)undefined undefined undefined undefined-undefined
[8] Sixsmith DJ(undefined)undefined undefined undefined undefined-undefined

← 1 →