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  • Ergodic Theory and Dynamical Systems, Volume 16, Issue 6
  • December 1996, pp. 1297-1310

Properties of attractors of generic homeomorphisms

  • Mike Hurley (a1)
  • DOI:
  • Published online: 14 October 2010

We describe several generic properties of homeomorphisms on compact manifolds. These properties concern the attractors of a homeomorphism, its chain recurrent set, and the periodic points.

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[1] C. Conley . Isolated Invariant Sets and the Morse Index. C.B.M.S. publication #38, A.M.S., Providence, 1978.

[2] E. M. Coven , J. Madden and Z. Nitecki . A note on generic properties of continuous maps. Ergodic Theory and Dynamical Systems II. Birkhäuser, Boston, 1982, pp. 97101.

[4] J. Franks . A variation of the Poincaré-Birkhoff theorem. Hamiltonian Dynamical Systems (Contemp. Math. vol. 81) A.M.S., Providence, 1988, pp. 111117.

[5] M. Hurley . Noncompact chain recurrence and attraction. Proc. A.M.S. 115 (1992), 11391148.

[6] M. Hurley . Generic homeomorphisms have no smallest attractors. Proc. A.M.S. 123 (1995), 12771280.

[7] M. Hurley . On proofs of the C0 general density theorem. Proc. A.M.S. 124 (1996), 13051309.

[9] J. Munkres . Obstructions to the smoothing of piecewise-differentiable homeomorphisms. Ann. Math. 72 (1960), 521554.

[10] Z. Nitecki and M. Shub . Filiations, decompositions, and explosions. Amer. J. Math. 97 (1976), 10291047.

[11] J. Palis , C. Pugh , M. Shub and D. Sullivan . Genericity theorems in topological dynamics. Dynamical Systems—Warwick 1974 (Lecture Notes in Mathematics 468), Springer, New York, 1975, pp. 241250.

[12] M. Shub . Structurally stable diffeomorphisms are dense. Bull. A.M.S. 78 (1972), 817818.

[14] P. Walters . On the pseudo-orbit tracing property and its relationship to stability. The Structure of Attractors in Dynamical Systems (Lecture Notes in Mathematics 668). Springer, New York, 1978, pp. 231244.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
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