Perturbations of rational Misiurewicz maps
Magnus Aspenberg

TL;DR
This paper studies how rational Misiurewicz maps behave under perturbations, showing that non-Lattes Misiurewicz maps can be approximated by hyperbolic maps, with implications for complex dynamics.
Contribution
It demonstrates that non-Lattes rational Misiurewicz maps with full Julia set can be approximated by hyperbolic maps, expanding understanding of their stability.
Findings
Non-Lattes Misiurewicz maps can be approximated by hyperbolic maps.
The Julia set being the entire sphere is a key condition.
Perturbation properties differ for Lattes and non-Lattes maps.
Abstract
In this paper we investigate the perturbation properties of rational Misiurewicz maps, when the Julia set is the whole sphere (the other case is treated in [1]). In particular, we show that if f is a Misiurewicz map and not a flexible Lattes map, then we can find a hyperbolic map arbitrarily close to f.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Advanced Differential Geometry Research
