On groups of formal diffeomorphisms of several complex variables

On Groups of Diffeomorphisms

I. We consider here the groups of homeomorphisms on Euclidean w-space and the «-sphere Sn. Chiefly we will be concerned with the question of whether or not these groups reduce in an homotopy sense to the ordinary orthogonal group acting on these spaces. Such questions are intimately connected with the theory of fibre bundles in which these spaces occur as fibres. We will restrict ourselves to t...

Lecture notes on several complex variables

Some inequalities in connection to relative orders of entire functions of several complex variables

Let f, g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

Formal Laurent series in several variables

We explain the construction of fields of formal infinite series in several variables, generalizing the classical notion of formal Laurent series in one variable. Our discussion addresses the field operations for these series (addition, multiplication, and division), the composition, and includes an implicit function theorem.

Complex Dynamics in Several Variables

1. Motivation 117 2. Iteration of Maps 118 3. Regular Versus Chaotic Behavior 119 4. The Horseshoe Map and Symbolic Dynamics 120 5. Hénon Maps 123 6. Properties of Horseshoe and Hénon Maps 126 7. Dynamically Defined Measures 127 8. Potential Theory 129 9. Potential Theory in One-Variable Dynamics 131 10. Potential Theory and Dynamics in Two Variables 133 11. Currents and Applications to Dynamic...