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# Dynamic Tessellations Associated with Cubic Polynomials

## [HYBRID WORKSHOP] Connections Workshop: Complex Dynamics - from special families to natural generalizations in one and several variables February 02, 2022 - February 04, 2022

February 02, 2022 (10:00 AM PST - 10:50 AM PST)
Speaker(s): Araceli Bonifant (University of Rhode Island)
Location: MSRI: Online/Virtual
Tags/Keywords
• cubic polynomials

• parameter rays

• dynamic rays

• tessellations

• escape regions

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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#### Dynamic Tessellations Associated With Cubic Polynomials

Abstract

We study cubic polynomial maps from $\C$ to $\C$ with a critical orbit of period $p$. For each $p>0$ the space of conjugacy classes of such maps forms a smooth Riemann surface with a smooth compactification $\overline S_p$. For each $q>0$ I will describe a dynamically defined tessellation of $\overline S_p$. Each face of this tessellation corresponds to one particular behavior for periodic orbits of period $q$. (Joint work with John Milnor.)

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