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1	Lower ramification numbers of wildly ramified power series Fransson, Jonas January 2014 (has links) In this thesis we study lower ramification numbers of power series tan- gent to the identity that are defined over fields of positive characteristics. Let f be such a series, then f has a fixed point at the origin and the corresponding lower ramification numbers of f are then, up to a constant, the multiplicity of zero as a fixed point of iterates of f. In this thesis we classify power series having ‘small’ ramification numbers. The results are then used to study ramification numbers of polynomials not tangent to the identity. We also state a few conjectures motivated by computer experiments that we performed. Lower ramification numbers Minimal ramification Ramified polynomials Ramified power series Difference equations Recurrence relations Optimal cycles Periodic points
2	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

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Lower ramification numbers of wildly ramified power series

Ramification of polynomials