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

Igors Gorbovickis

Published 2013-05-04Version 1

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.