岡本 久

We consider mappings of one real and two complex variables with a range in two dimensional complex space. We introduce the notion of O(2)-equivariance with mode (m, n), where m and n are distinct positive integers. We consider only O(2)-equivariant mappings with mode (1, 2). Normal forms and universal unfoldings are given in three cases ; one is a generic case, the other two cases deal with some degeneracies.

A free boundary problem for a flow around a circle is analyzed. We find and mathematically prove that bifurcations from the trivial flow actually take place. Golubitsky‐Schaeffer theory, together with a formula concerning variations of domains, enables us to clarify the behaviors of the branches of nontrivial solutions. Copyright © 1984 John Wiley &amp Sons, Ltd

Free boundary problems for flows circulating around a circle or sphere are considered. It is revealed that the surface tension plays a crucial role concerning perturbations and bifurcations of a trivial flow. Main tools are implicit function theorems (classical or generalized) and bifurcation theory due to Sattinger or Golubitsky&amp Schaeffer. Therefore all the classical solution near the trivial one are dealt with. © 1983, Publishing Committee of Lecture Notes in Numerical and Applied Analysis.