On the Geometries of the Rational Unfoldings of
W. Kuyk (in real life, Willem Kuijk - here are a few other
of his many works) and
Applicandae Mathematicae, volume 19 (1990), pages 77-86.
With a view to applications to self-regulating dynamical processes in biology,
we determine the geometric structure of what we call 'isotangent curves',
i.e., curves parametrized by the slopes of their points. They come up
naturally as bifurcation curves of rational unfoldings of Xk
classify them according to degree and number of cusps. They, as well as
their isotangent involute curves, turn up in simulations of these processes.
AMS Subject Classifications (1985)
52A10, 28A75, 26B15.
There are a few reprints left. If your library does not have this
particular journal issue, ask for a reprint by emailing me your postal address.
Remove "unwanted" from the address below.
- Bröcker, Th. and Lander, L., "Differential Germs and Catastrophes,"
Cambridge University Press, Cambridge 1975.
- Guggenheimer, H.W., "Differential Geometry," McGraw-Hill, New York 1973.
- Janssens, J. and Kuyk, W., A Set of Integral-differential Equations
for the Ventricular Cardiac Suction Pump, in B. Schmidt (ed.), "Proc. 3rd
European Simulation Congress," Erlangen 1990, pp. 567-572.
- Kuyk, Willem, The Human Thermostat:
a Catastrophe Type Controlling Biological Processes,
pp. 713-719 in Vansteenkiste, G.C., Kerckhoffs,
E.J.H., Dekker, L. and Zuidervaart, J.C. (eds.),
Proceedings of the Second European Simulation Congress," Antwerp 1986.
- Kuyk, Willem, Servocontrol of the Heart Rate in Homeothermic Animals,
Bull. Math. Biol. 48 (1986), 107-124.
- Kuyk, Willem and Smits, Lieven,
Rational Unfoldings of ±Xk
and Their Relation
with Geometric Equilibrium Theory, Acta Applic. Math. 19
- Poston, T. and
"Catastrophe Theory and its Applications,"
Pitman, London 1978.
"Catastrophe Theory: Selected Papers 1972-1977,"
Addison-Wesley, Reading, Mass. 1977.
History of this page
- Sep-Oct 2002: move to new site and update contact information
- 25 May 1998: add list of references
- 7 May 1998: include other information about the paper
- 1 Apr 1998: creation of the abstract