Rational Misiurewicz maps for which the Julia set is not the whole sphere

TL;DR

This paper demonstrates that certain Misiurewicz maps with non-whole sphere Julia sets are Lebesgue density points of hyperbolic maps, revealing a nuanced structure in complex dynamics.

Contribution

It establishes a new density property of Misiurewicz maps within the space of hyperbolic maps, expanding understanding of their distribution.

Findings

Misiurewicz maps with non-whole sphere Julia sets are Lebesgue density points of hyperbolic maps.

The result links the structure of Misiurewicz maps to hyperbolic dynamics.

Provides insights into the geometric and measure-theoretic properties of Julia sets.

Abstract

We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.