JP Journal of Algebra, Number Theory and Applications
Volume 29, Issue 2, Pages 189 - 206
(June 2013)
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MULTIPLIER SPECTRA AND THE MODULI SPACE OF DEGREE 3 MORPHISMS ON
Benjamin Hutz and Michael Tepper
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Abstract: The moduli space of degree d morphisms on has received much study. McMullen showed that, except for certain families of Lattès maps, there is a finite-to-one correspondence between classes of morphisms in the moduli space and the multipliers of the periodic points. For degree 2 morphisms, Milnor and Silverman showed that the correspondence is an isomorphism [8, 10]. In this article, we address two cases with algebraic methods: polynomial maps of any degree and rational maps of degree 3. |
Keywords and phrases: moduli space, dynamical systems, McMullen’s theorem, multiplier spectrum. |
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