Bifurcation Currents in Holomorphic Families of Rational Maps

By Franccois Berteloot. 2012

49 citations recorded by the source corpus.

These lectures are devoted to the study of bifurcations within holomorphic families of rational maps or polynomials by mean of ergodic and potential theoretic tools. After giving a general overview of the subject, we consider rational functions as ergodic dynamical systems and introduce the Green measure of a rational map and study the properties of its Lyapunov exponent. Next we consider Holomorphic families and introduce the class of hypersurfaces (Pern(w)) in the parameter space of a holomorphic family and study the connectedness locus in polynomial families. Then we introduce the bifurcation current and discuss equidistribution towards the bifurcation current and the self-intersection of the bifurcation current.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/35819d6468e27d566c443d51a81c82ede8e8f28d

Citations in the corpus

• Distribution of postcritically finite polynomials (2013, unknown): “ures d−(k1(n)+···+kd−1(n)) (d−1)!(2π)d−1 Z [0,2π]d−1 d^−1 j=1 [Per∗(kj(n),reiθj)]dθ1 ···dθd−1 converge to the bifurcation measure for a suitable choice of increasing functions kj : N→ N (compare with [B]). Inspired by the seminal work of Briend and Duval [BD2] on the construction of the measure of m”