Lower ramification numbers of wildly ramified power series

• Main Author: Fransson, Jonas
• Format: Others
• Language: English
• Published: Linnéuniversitetet, Institutionen för matematik (MA) 2014
• Subjects: Lower ramification numbers; Minimal ramification; Ramified polynomials; Ramified power series; Difference equations; Recurrence relations; Optimal cycles; Periodic points
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-35313

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.