A degenerate Newton’s map in two complex variables: Linking with currents

A degenerate Newton’s Map in two complex variables: linking with currents

Little is known about the global structure of the basins of attraction of Newton’s method in two or more complex variables. We make the first steps by focusing on the specific Newton mapping to solve for the common roots of P (x, y) = x(1− x) and Q(x, y) = y +Bxy − y. There are invariant circles S0 and S1 within the lines x = 0 and x = 1 which are superattracting in the x-direction and hyperbol...

Dynamics of a Quadratic Map in Two Complex Variables

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...

Growth analysis of entire functions of two complex variables

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Conformality in Connection with Functions of Two Complex Variables

Numerical Investigation of the Structure of Density Currents in a two Dimensional Channel