On the generic nonexistence of first integrals
HTML articles powered by AMS MathViewer
- by Mike Hurley PDF
- Proc. Amer. Math. Soc. 98 (1986), 142-144 Request permission
Abstract:
The property of having no ${C^n}$ first integrals other than constants is shown to be generic in ${\operatorname {Diff} ^r}(M)$ for each $r = 1,2, \ldots$, where $n$ is the dimension of $M$.References
- J. L. Arraut, Note on structural stability, Bull. Amer. Math. Soc. 72 (1966), 542–544. MR 195108, DOI 10.1090/S0002-9904-1966-11535-5
- M. M. Peixoto, Qualitative theory of differential equations and structural stability, Differential Equations and Dynamical Systems (Proc. Internat. Sympos., Mayaguez, P.R., 1965) Academic Press, New York, 1967, pp. 469–480. MR 0221015
- Charles C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967), 1010–1021. MR 226670, DOI 10.2307/2373414
- R. Clark Robinson, Generic properties of conservative systems, Amer. J. Math. 92 (1970), 562–603. MR 273640, DOI 10.2307/2373361
- Floris Takens, On Zeeman’s tolerance stability conjecture, Manifolds–Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, 1971, pp. 209–219. MR 0279790
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 142-144
- MSC: Primary 58F10; Secondary 58F35
- DOI: https://doi.org/10.1090/S0002-9939-1986-0848891-7
- MathSciNet review: 848891