×

Isolated invariant sets and isolating blocks. (English) Zbl 0223.58011


MSC:

37C10 Dynamics induced by flows and semiflows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] G. D. Birkhoff, “Nouvelles recherches sur les systèmes dynamiques,” in Collected works. Vol. 2, Amer. Math. Soc., Providence, R. I., 1950, pp. 530-659.
[2] C. Conley, “Invariant sets in a monkey saddle,” Proceedings United States-Japan seminar on differential and functional equations, Edited by William A. Harris Jr. and Yasutaka Sibuya, Benjamin, New York, 1967. MR 36 #5415.
[3] C. C. Conley, The retrograde circular solutions of the restricted three-body problem via a submanifold convex to the flow, SIAM J. Appl. Math. 16 (1968), 620 – 625. · Zbl 0159.55104 · doi:10.1137/0116050
[4] Charles C. Conley, On the ultimate behavior of orbits with respect to an unstable critical point. I. Oscillating, asymptotic, and capture orbits, J. Differential Equations 5 (1969), 136 – 158. · Zbl 0169.11402 · doi:10.1016/0022-0396(69)90108-9
[5] C. Conley, Twist mappings, linking, analyticity, and periodic solutions which pass close to an unstable periodic solution, Topological dynamics (Sympos., Colorado State Univ., Ft. Collins, Colo., 1967) Benjamin, New York, 1968, pp. 129 – 153. · Zbl 0208.35403
[6] C. Conley and R. Easton, Isolated invariant sets and isolating blocks, Advances in differential and integral equations (Conf. Qualitative Theory of Nonlinear Differential and Integral Equations, Univ. Wisconsin, Madison, Wis., 1968; in memoriam Rudolph E. Langer (1894 – 1968)), Soc. Indust. Appl. Math., Philadelphia, Pa., 1969, pp. 97 – 104. Studies in Appl. Math., No. 5. · Zbl 0223.58011
[7] Robert W. Easton, On the existence of invariant sets inside a submanifold convex to a flow, J. Differential Equations 7 (1970), 54 – 68. · Zbl 0185.27501 · doi:10.1016/0022-0396(70)90123-3
[8] R. W. Easton, Locating invariant sets, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 55 – 59.
[9] Robert W. Easton, On the existence of invariant sets inside a submanifold convex to a flow, J. Differential Equations 7 (1970), 54 – 68. · Zbl 0185.27501 · doi:10.1016/0022-0396(70)90123-3
[10] -, “A flow near a degenerate critical point,” Advances in differential and integral equations, Edited by John Nohel, Benjamin, New York, p. 137.
[11] Jürgen Moser, A rapidly convergent iteration method and non-linear differential equations. II, Ann. Scuola Norm. Sup. Pisa (3) 20 (1966), 499 – 535. · Zbl 0144.18202
[12] Robert J. Sacker, A perturbation theorem for invariant Riemannian manifolds, Differential Equations and Dynamical Systems (Proc. Internat. Sympos., Mayaguez, P.R., 1965) Academic Press, New York, 1967, pp. 43 – 54.
[13] Robert J. Sacker, A new approach to the perturbation theory of invariant surfaces, Comm. Pure Appl. Math. 18 (1965), 717 – 732. · Zbl 0133.35501 · doi:10.1002/cpa.3160180409
[14] Stephen Smale, Diffeomorphisms with many periodic points, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 63 – 80.
[15] Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. · Zbl 0145.43303
[16] Taro Ura, On the flow outside a closed invariant set; stability, relative stability and saddle sets, Contributions to Differential Equations 3 (1964), 249 – 294.
[17] T. Ważewski, Sur une méthode topologique de l’examen de l’allure asymptotique des intégrales des équations différentielles, Proc. Internat. Congress Math. (Amsterdam, 1954) vol. III, Noordhoff, Groningen and North-Holland, Amsterdam, 1956, pp. 132-139. MR 19, 272.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.