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Transactions of the American Mathematical Society

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Isolated invariant sets and isolating blocks


Authors: C. Conley and R. Easton
Journal: Trans. Amer. Math. Soc. 158 (1971), 35-61
MSC: Primary 57.48
DOI: https://doi.org/10.1090/S0002-9947-1971-0279830-1
MathSciNet review: 0279830
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  • [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. MR 0227529, https://doi.org/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. MR 0251301, https://doi.org/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. MR 0293203
  • [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. MR 0397793
  • [7] Robert W. Easton, On the existence of invariant sets inside a submanifold convex to a flow, J. Differential Equations 7 (1970), 54–68. MR 0249755, https://doi.org/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. MR 0270398
  • [9] Robert W. Easton, On the existence of invariant sets inside a submanifold convex to a flow, J. Differential Equations 7 (1970), 54–68. MR 0249755, https://doi.org/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. MR 0206461
  • [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. MR 0218700
  • [13] Robert J. Sacker, A new approach to the perturbation theory of invariant surfaces, Comm. Pure Appl. Math. 18 (1965), 717–732. MR 0188566, https://doi.org/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. MR 0182020
  • [15] Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
  • [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. MR 0163018
  • [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.

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DOI: https://doi.org/10.1090/S0002-9947-1971-0279830-1
Article copyright: © Copyright 1971 American Mathematical Society