Let f : C −→ C be a polynomial. The bifurcation set B for f is the minimal set of points of C such that f : C \f−1(B) −→ C\B is a locally trivial fibration. For c ∈ C, we denote the fiber f−1(c) by Fc. The fiber Fc is irregular if c is in B. If s / ∈ B, then Fs is a generic fiber and is denoted by Fgen . The tube Tc for the value c is a neighborhood f −1(D2 ε(c)) of the fiber Fc, where D 2 ε(c)...

In this work we prove a new Lp holomorphic extension result for functions defined on product Lipschitz surfaces with small Lipschitz constants in two complex variables. We define biparameter and partial Cauchy integral operators that play the role of boundary values for holomorphic functions on product Lipschitz domain. In the spirit of the application of David-Journé-Semmes [DJS85] and Christ’...

We study the map 9: C!C defined by 9(w, z)=(z, z+w) and the associated collection of sequences [zj] satisfying the recurrence zj+2=zj+1+zj . Iteration of 9 is equivalent to the study of such sequences. We analyze growth rates of the sequences, positive sequences, periodic and asymptotically periodic sequences and establish the existence of doubly infinite homoclinic sequences, non-zero sequence...