We discuss when two rational functions f and g can have the same measure of maximal
entropy. The polynomial case was completed by Beardon, Levin, Baker–Eremenko, Schmidt …

We give a geometric description of the parabolic bifurcation locus in the space
$\operatorname {Rat} _d $ of all rational functions on $\mathbb {P}^ 1$ of degree $ d> 1 …

Let $ K $ be an algebraically closed field of characteristic 0 that is complete with respect to a
non-trivial and non-archimedean absolute value. We establish an approximation of the …

It is an open problem whether repelling periodic points are dense in the classical Julia set of
a non-archimedean rational function of degree more than one. We give a partial positive …

We establish a quantitative approximation formula of the Lyapunov exponent of a rational
function of degree more than one over an algebraically closed field of characteristic 0 0 that …

Let f be a rational function of degree d> 1 on the projective line over a possibly non-
archimedean algebraically closed field. A well-known process initiated by Brolin considers …

We establish a quantitative adelic equidistribution theorem for a sequence of effective
divisors on the projective line over the separable closure of a product formula field having …

We study a question on characterizing polynomials among rational functions of degree> 1>
1 on the projective line over an algebraically closed field that is complete with respect to a …

In the theory of dynamical systems, the notion of $\omega $-limit sets of points is classical. In
this paper, the existence of limit functions on subsets of the underlying space is treated. It is …

arXiv:1808.06278v1 [math.DS] 20 Aug 2018 Page 1 arXiv:1808.06278v1 [math.DS] 20 Aug
2018 A GENERALIZATION OF THE CONVERSE OF BROLIN’S THEOREM YÛSUKE …