Abstract
This paper is motivated by the problem of fitting a differential equation to experimental data; a first step is to fit the time 1 map of the corresponding flow, as described in Section 1, and these time 1 maps are the diffeomorphisms in the title of the present paper. The negative part of statement (ii) of Theorem 3.1 implies that there is no algorithm which fits diffeomorphisms of the plane to observed data in a way that depends continuously on the observed data and only on the observed data.
Similar content being viewed by others
References
E. Artin, “Theory of braids,”Annals of Mathematics 48 (1947) 101–126.
E.R. Fadell and L. Neuwirth, “Configuration spaces,”Mathematica Scandinavica 10 (1962) 111–118.
P.J. Hilton, “On the homotopy groups of the union of spheres,”Journal of the London Mathematical Society 30 (1955) 154–172.
J.W. Milnor,Morse Theory (Annals of Math. Studies 51, Princeton University Press, 1963).
R. Narasimhan,Analysis on Real and Complex Manifolds (Advanced Studies in Pure Mathematics, Masson & Cie, North-Holland 1973).
J.L. Noakes, “Feedback and accessibility,”IMA Journal of Mathematical Control of Information 2 (1985) 81–85.
J.L.Noakes, “Discrete signals and continuous dynamics,”IMA Journal of Mathematical Control & Information 3 (1986) 293–297.
J.L.Noakes, “Trajectory generation and obstacle avoidance,”IMA Journal of Mathematical Control & Information 4 (1987) 293–300.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Noakes, J.L. Fitting maps of the plane to experimental data. Mathematical Programming 43, 225–234 (1989). https://doi.org/10.1007/BF01582291
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01582291