A characterization of damped and undamped harmonic oscillations by a superposition property II.
A comparative study of functional equations characterising sine and cosine.
A factored form of complex analytic functions and its application to finding partial fraction decompositions.
A functional equation arising from the Joukowski transformation
A gallery of iterated correspondences.
A generalization of Hille's and Robinson's functional equations
A new functional equation characterizing generalized Joukowski transformations.
A new proceeding for solving of certain class of functional equations
A new Pythagorean functional equation.
A note on a functional inequality.
A note on a theorem of C. L. Siegel concerning Bessel's equation
A note on functional equations of the -adic polylogarithms
A note on the structure of quadratic Julia sets
In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present...
A inequality for Kleinian groups.
A parabolic Pommerenke-Levin-Yoccoz inequality
In a recent preprint [B], Bergweiler relates the number of critical points contained in the immediate basin of a multiple fixed point β of a rational map f: ℙ¹ → ℙ¹, the number N of attracting petals and the residue ι(f,β) of the 1-form dz/(z-f(z)) at β. In this article, we present a different approach to the same problem, which we were developing independently at the same time. We apply our method to answer a question raised by Bergweiler. In particular, we prove that when there are only...
A Proof of Simultaneous Linearization with a Polylog Estimate
We give an alternative proof of simultaneous linearization recently shown by T. Ueda, which connects the Schröder equation and the Abel equation analytically. In fact, we generalize Ueda's original result so that we may apply it to the parabolic fixed points with multiple petals. As an application, we show a continuity result on linearizing coordinates in complex dynamics.
About the growth of entire functions solutions of linear algebraic -difference equations
Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points.
An axiomatization of Nesterenko's method and applications on Mahler functions II
An equivalent property to Ivory's theorem from the standpoint of conformal mapping