Global ETD Search

1	Ramification of polynomials Strikic, Ana January 2021 (has links) In this research,we study iterations of non-pleasantly ramified polynomials over fields of positive characteristic and subsequently, their lower ramification numbers. Of particular interest for this thesis are polynomials for which both the multiplicity and the degree of its iterates grow exponentially. Specifically we consider the family of polynomials such that given a positive integer k the family is given by P(z) = z(1 + z (3^k-1)/2 + z3^k-1). The cubic polynomial z + z2 + z3 is a special case of this family and is particularly interesting. non-pleasantly ramified polynomials minimally ramified polynomial lower ramification numbers minimal ramification discrete dynamical systems iterating polynomials ultrametric fields Discrete Mathematics Diskret matematik