Completely unstable flows on 2-manifolds

Neumann, Dean A.

doi:10.1090/S0002-9947-1977-0448440-0

Completely unstable flows on -manifolds

Author: Dean A. Neumann
Journal: Trans. Amer. Math. Soc. 225 (1977), 211-226
MSC: Primary 58F10
DOI: https://doi.org/10.1090/S0002-9947-1977-0448440-0
MathSciNet review: 0448440
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Abstract: Completely unstable flows on 2-manifolds are classified under both topological and ${C^r}$ -equivalence $(1 \leqslant r \leqslant \infty )$ , in terms of the corresponding orbit spaces.

[1] N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Die Grundlehren der mathematischen Wissenschaften, Band 161, Springer-Verlag, New York-Berlin, 1970. MR 0289890
[2] André Haefliger and Georges Reeb, Variétés (non séparées) à une dimension et structures feuilletées du plan, Enseignement Math. (2) 3 (1957), 107–125 (French). MR 0089412
[3] Otomar Hájek, Sections of dynamical systems in 𝐸², Czechoslovak Math. J. 15 (90) (1965), 205–211 (English, with Russian summary). MR 0176181
[4] Wilfred Kaplan, Regular curve-families filling the plane, I, Duke Math. J. 7 (1940), 154–185. MR 0004116
[5] Lawrence Markus, Parallel dynamical systems, Topology 8 (1969), 47–57. MR 0234489, https://doi.org/10.1016/0040-9383(69)90030-5
[6] James Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math. (2) 72 (1960), 521–554. MR 0121804, https://doi.org/10.2307/1970228
[7] Dean Neumann, Smoothing continuous flows, J. Differential Equations 24 (1977), no. 1, 127–135. MR 0431280, https://doi.org/10.1016/0022-0396(77)90173-5
[8] T. Ważewski, Sur un problème de caractère intégral relatif à l'équation $\partial z/\partial x + Q(x,y)\partial z/\partial y = 0$ , Mathematica 8 (1934), 103-116.