We give a method for constructing transcendental entire functions with good control of both the singular values of$f$and the geometry of$f$. Among other applications, we construct a function$f$with bounded singular set, whose Fatou set contains a wandering domain.

No abstract uploaded!

We study groups of automorphisms and birational transformations of quasi-projective varieties. Two methods are combined; the first one is based on p-adic analysis, the second makes use of isoperimetric inequalities and Lang–Weil estimates. For instance, we show that, if SLn(Z) acts faithfully on a complex quasi-projective variety X by birational transformations, then dim(X)⩾n−1 and X is rational if dim(X)=n−1.

This paper presents a 2×2 dynamical system to study the cyclic appearance and disappearance of the gas phase in a two-component (CO2, H2O), two phase (gas, liquid) flow in a single pore. Depending on injection rate, linearization of the dynamical system around equilibrium shows that the gas phase can exhibit two behaviors, either cyclically vanishing and appearing, or approaching a steady-state volume value. Numerical simulations were also run on the fully non-linear dynamical system to verify the results of the linearized model.

The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis. Motivated by results of Bangert and applications in turbulent combus- tion, we show that when the dimension is two and the flow of the ambient fluid is either weak or very strong, the level set of the effective burning velocity has flat pieces. Due to the lack of an applicable Hopf-type rigidity result, we need to identify the exact location of at least one flat piece. Implications on the effective flame front and other related inverse type problems are also discussed.