Captures, matings and regluings
Inna Mashanova, Vladlen Timorin
TL;DR
This paper investigates the structure of parameter slices in quadratic rational functions, identifying specific arcs formed by matings of quadratic polynomials on the boundaries of hyperbolic components.
Contribution
It introduces a method to identify arcs in parameter slices that are represented by matings of quadratic polynomials, enhancing understanding of the boundary structure.
Findings
Arcs correspond to matings of quadratic polynomials.
These arcs lie on the boundaries of hyperbolic components.
The work clarifies the structure of parameter slices in quadratic rational functions.
Abstract
In parameter slices of quadratic rational functions, we identify arcs represented by matings of quadratic polynomials. These arcs are on the boundaries of hyperbolic components.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Functional Equations Stability Results