2009/08/23 by Dmitry Khavinson, Erik Lundberg, Khavinson, Dmitry +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #math-ph #math.CV #math.MP
paper · pdf · doi:10.48550/arxiv.0908.3310
11 pages, 3 figures
arxiv created 2009/08/23 · openalex publication_date 2009/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the Schwarz function of an ellipse, it was recently shown that galaxies with density constant on confocal ellipses can produce at most four ``bright'' images of a single source. The more physically interesting example of an isothermal galaxy has density that is constant on homothetic ellipses. In that case bright images can be seen to correspond to zeros of a certain transcendental harmonic mapping. We use complex dynamics to give an upper bound on the total number of such zeros.