Hyperbolic components of cosine family with a fixed critical point

arXiv (Cornell University) 2026 Preprint Open access

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Authors: WeiYuan QIU, Lingrui Wang
DOI: 10.48550/arxiv.2603.10554
Cited by: 0

Abstract

We studied the parameter plane of the cosine functions with a fixed critical point. The hyperbolic components can be classified into three types: A, C and D. All the hyperbolic components are bounded and simply connected, except for the unique type-A component, which contains 0 as an isolated boundary point. Using the method of para-puzzle, we constructed a phase-parameter transfer mapping and proved that the boundaries of hyperbolic components are Jordan curves. By a similar idea, the hyperbolic components of type C are quasidisks.

Fields of Study & Subjects

Mathematical Dynamics and Fractals Analytic and geometric function theory Advanced Differential Equations and Dynamical Systems

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 March 2026
Language
EN
Document type
Preprint