Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable

Abstract

We consider a space of complex polynomials of degree $n\ge 3$ with $n-1$ distinguished periodic orbits. We prove that the multipliers of these periodic orbits considered as algebraic functions on that space, are algebraically independent over the field of complex numbers.

Cited by in corpus (5)

• The Moduli Space of Polynomial Maps and Their Fixed-Point Multipliers: II. Improvement to the Algorithm and Monic Centered Polynomials
• The Moduli Space of Polynomial Maps and Their Holomorphic Indices: I. Generic Properties in the Case of Having Multiple Fixed Points
• Critical points of the multiplier map for the quadratic family
• Spaces of polynomials related to multiplier maps
• Parameterizing degree n polynomials by multipliers of periodic orbits