23 citations · 149 across the 28 of their papers we have counts for
4 papers · 1 filter
Degenerations of Complex Dynamical Systems II: Analytic and Algebraic Stability
Laura DeMarco, Xander Faber, with an appendix by Jan Kiwi
We study pairs consisting of a non-Archimedean rational function and a finite set of vertices in the Berkovich projective line, under a certain stability hypothesi…
Preperiodic points for quadratic polynomials over quadratic fields
John R. Doyle, Xander Faber, David Krumm
To each quadratic number field and each quadratic polynomial with -coefficients, one can associate a finite directed graph whose vertices are the -rational p…
Benedetto's trick and existence of rational preperiodic structures for quadratic polynomials
Xander Faber
We refine a result of R. Benedetto in p-adic analysis in order to exhibit infinitely many quadratic polynomials with rational coefficients having a specified graph of rational prep…
Degenerations of Complex Dynamical Systems
Laura DeMarco, Xander Faber
We show that the weak limit of the maximal measures for any degenerating sequence of rational maps on the Riemann sphere must be a countable sum of atoms. For a 1-parameter family…