37 citations · 77 across the 8 of their papers we have counts for
12 papers
Generalizations of Douady's magic formula
Adam Epstein, Giulio Tiozzo
We generalize a combinatorial formula of Douady from the main cardioid to other hyperbolic components of the Mandelbrot set, constructing an explicit piecewise linear map which…
Tips of Tongues in the Double Standard Family
Kuntal Banerjee, Xavier Buff, Jordi Canela +1
We answer a question raised by Misiurewicz and Rodrigues concerning the family of degree 2 circle maps defined by \[F_λ(x) := 2…
Rational maps with a preperiodic critical point
Xavier Buff, Adam L. Epstein, Sarah Koch
We show that the set of conjugacy classes of cubic polynomials with a prefixed critical point, of preperiod , is an irreducible algebraic curve. We also establish an analo…
Eigenvalues of the Thurston operator
Xavier Buff, Adam L. Epstein, Sarah Koch
Let be a postcritically finite rational map. Let be the space of meromorphic quadratic differentials on $ \hat{…
On invariance of order and the area property for finite-type entire functions
Adam Epstein, Lasse Rempe-Gillen
Let f be an entire function that has only finitely many critical and asymptotic values. Up to topological equivalence, the function is determined by combinatorial information,…
On Thurston's pullback map
Xavier Buff, Adam Epstein, Sarah Koch +1
Let f: P^1 \to P^1 be a rational map with finite postcritical set P_f. Thurston showed that f induces a holomorphic map σ_f of the Teichmueller space T modelled on P_f to itself fi…