The projective translation equation, the 2-dimensional superflow, and the elliptic curve xy(x-y)=c

Details The projective translation equation, the 2-dimensional superflow, and the elliptic curve xy(x-y)=c The projective translation equation, the 2-dimensional superflow, and the elliptic curve xy(x-y)=c

2012-02-17

arxiv.org/abs/1202.3958v1

Mathematics

Algebraic Geometry

6 pages. This is the introduction to the forthcoming main paper, which will be submitted as v2

Scientific paper

In this paper we investigate the unique function Lambda(x,y) which defines the flow in the plane and satisfies these main properties: it is a homeomorphism of a real plane suitably compactified with three curves; it satisfied the linear first order PDE and the iterative functional equation, which we earlier named the projective translation equation - the latter is a special case of the well-known translation equation - and thus Lambda is the flow; this function also posseses a 6-fold symmetry; it parametrizes the family of elliptic curves xy(x-y)=c. Further, we also discuss the complex version of this flow. The analysis of the function Lambda is intricately related with the geometry of the Riemann surface of the function [z(1-z)]^(-1/3), also with the associated abelian integral and its periods. We call this function Lambda the 2-dimensional superflow. We also introduce analogous superflows for higher dimensions.

Affiliated with

Also associated with

No associations

Rating

The projective translation equation, the 2-dimensional superflow, and the elliptic curve xy(x-y)=c does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The projective translation equation, the 2-dimensional superflow, and the elliptic curve xy(x-y)=c, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The projective translation equation, the 2-dimensional superflow, and the elliptic curve xy(x-y)=c will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-36373