Copyright © 2011 Yelena Kozmina and Felix Sadyrbaev. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider equation , where is a polynomial,
allowing the equation to have multiple period annuli. We detect the
maximal number of possible period annuli for polynomials of odd degree and
show how the respective optimal polynomials can be constructed.