Abstract
AbstractTaking the hint from usual parametrization of circle and hyperbola, and inspired by the pathwork initiated by Cayley and Dixon for the parametrization of the “Fermat” elliptic curve $$x^3+y^3=1$$
x
3
+
y
3
=
1
, we develop an axiomatic study of what we call “Keplerian maps”, that is, functions $${{\,\mathrm{{\mathbf {m}}}\,}}(\kappa )$$
m
(
κ
)
mapping a real interval to a planar curve, whose variable $$\kappa $$
κ
measures twice the signed area swept out by the O-ray when moving from 0 to $$\kappa $$
κ
. Then, given a characterization of k-curves, the images of such maps, we show how to recover the k-map of a given parametric or algebraic k-curve, by means of suitable differential problems.
Funder
Alma Mater Studiorum - Università di Bologna
Publisher
Springer Science and Business Media LLC
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