David Sumner Lipham

activity

20162024

most citedThe topological dimension of radial Julia sets

7 citations · 38 across the 19 of their papers we have counts for

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4 papers · 1 filter

math.DS2020★ 2 cited

Distinguishing endpoint sets from Erdős space

David S. Lipham

We prove that the set of all endpoints of the Julia set of $f (z) = exp (z) - 1$ which escape to infinity under iteration of $f$ is not homeomorphic to the rational Hilbert space $\math…

math.DS2020★ 1 cited

Erdős space in Julia sets

David S. Lipham

We prove that the rational Hilbert space $E$ , known as Erdős space, surfaces in complex dynamics via iteration of $e^{z} - 1$ .

math.DS2020★ 7 cited

The topological dimension of radial Julia sets

David S. Lipham

We prove that the meandering set for $f_{a} (z) = e^{z} + a$ is homeomorphic to the space of irrational numbers whenever $a$ belongs to the Fatou set of $f_{a}$ . This extends recent results b…

math.DS2019★ 2 cited

A note on the topology of escaping endpoints

David Sumner Lipham

We study topological properties of the escaping endpoints and fast escaping endpoints of the Julia set of complex exponential $exp (z) + a$ when $a \in (- \infty, - 1)$ . We show neither…