Rational Functions with Prescribed Critical Points

On Rational Maps with Two Critical Points

This is a preliminary investigation of the geometry and dynamics of rational maps with only two critical points.

Critical Notice Rational Starting Points

Epistemic justification has been claimed to be a special case of argument by philosophers such as Accordingly for each attempt, epistemic justification is the occasion of the arguer making a case for some conclusion based on other premises, when the audience and the arguer are the same person. The dialectical model of argument is used to inform how it is that a subject could come to justify her...

Weighted Turán Type Inequality for Rational Functions with Prescribed Poles

Firstly, we introduce a new type of weight functions named as N-doubling weights, which is an essential generalization of the well known doubling weights. Secondly, we establish a weighted Turán type inequality with N-doubling weights and a Nikolskii-Turán type inequality for rational functions with prescribed poles. Our results generalize some known Turán type inequality both for polynomials a...

Rational Functions with a Unique Critical Point

Over an algebraically closed field of positive characteristic, there exist rational functions with only one critical point. We give an elementary characterization of these functions in terms of their continued fraction expansions. Then we use this tool to discern some of the basic geometry of the space of unicritical rational functions, as well as its quotients by the SL2-actions of conjugation...

Critical points of simple functions