## Plugging flows

HTML articles powered by AMS MathViewer

- by Peter B. Percell and F. Wesley Wilson PDF
- Trans. Amer. Math. Soc.
**233**(1977), 93-103 Request permission

## Abstract:

A plug construction is a local modification of a nonsingular flow which severs certain kinds of recurrence properties. In this paper we investigate the effect of plug constructions on minimal sets, the nonwandering set, and the chain recurrent set and the explosions of these sets when a plug construction is perturbed.## References

- F. Wesley Wilson Jr.,
*On the minimal sets of non-singular vector fields*, Ann. of Math. (2)**84**(1966), 529–536. MR**202155**, DOI 10.2307/1970458 - F. Wesley Wilson Jr.,
*Singularities and periodic solutions which do not attract*, J. Differential Equations**8**(1970), 488–493. MR**276556**, DOI 10.1016/0022-0396(70)90020-3 - Charles C. Pugh, Russell B. Walker, and F. Wesley Wilson Jr.,
*On Morse-Smale approximations–a counterexample*, J. Differential Equations**23**(1977), no. 1, 173–182. MR**436218**, DOI 10.1016/0022-0396(77)90140-1 - F. B. Fuller,
*Note on trajectories in a solid torus*, Ann. of Math. (2)**56**(1952), 438–439. MR**51990**, DOI 10.2307/1969652 - Paul A. Schweitzer,
*Counterexamples to the Seifert conjecture and opening closed leaves of foliations*, Ann. of Math. (2)**100**(1974), 386–400. MR**356086**, DOI 10.2307/1971077 - Peter Percell,
*Presentations of $3$-manifolds arising from vector fields*, Trans. Amer. Math. Soc.**221**(1976), no. 2, 361–377. MR**407857**, DOI 10.1090/S0002-9947-1976-0407857-X - Ralph Abraham and Joel Robbin,
*Transversal mappings and flows*, W. A. Benjamin, Inc., New York-Amsterdam, 1967. An appendix by Al Kelley. MR**0240836** - John Milnor,
*Lectures on the $h$-cobordism theorem*, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR**0190942**, DOI 10.1515/9781400878055 - M. M. Peixoto,
*On an approximation theorem of Kupka and Smale*, J. Differential Equations**3**(1967), 214–227. MR**209602**, DOI 10.1016/0022-0396(67)90026-5 - Charles Pugh and Michael Shub,
*The $\Omega$-stability theorem for flows*, Invent. Math.**11**(1970), 150–158. MR**287579**, DOI 10.1007/BF01404608 - Peter B. Percell,
*Structural stability on manifolds with boundary*, Topology**12**(1973), 123–144. MR**322906**, DOI 10.1016/0040-9383(73)90002-5 - David L. Rod,
*Pathology of invariant sets in the monkey saddle*, J. Differential Equations**14**(1973), 129–170. MR**328220**, DOI 10.1016/0022-0396(73)90082-X - Robert W. Easton,
*Isolating blocks and symbolic dynamics*, J. Differential Equations**17**(1975), 96–118. MR**370663**, DOI 10.1016/0022-0396(75)90037-6
J. Yorke, Lecture at Univ. of California, Berkeley, 1975.
- Richard H. Elderkin,
*Separatrix structure for elliptic flows*, Amer. J. Math.**97**(1975), 221–247. MR**370661**, DOI 10.2307/2373669
—,

*Separatrix structure for regions attracted to solitary periodic solutions*, Proc. Internat. Sympos. Differential Equations (Brown Univ., 1974) (to appear). C. Conley,

*The gradient structure of a flow*(to appear).

## Additional Information

- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**233**(1977), 93-103 - MSC: Primary 58F10
- DOI: https://doi.org/10.1090/S0002-9947-1977-0448441-2
- MathSciNet review: 0448441