Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Shadowing property for inverse limit spaces

Authors: Liang Chen and Shi Hai Li
Journal: Proc. Amer. Math. Soc. 115 (1992), 573-580
MSC: Primary 58F10; Secondary 28D05, 54H20, 58F08
MathSciNet review: 1097338
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the relationship between the shadowing property for continuous maps on a compact metric space and that for the shift maps on the inverse limit spaces. As an example, we show that the shift map of some pseudoarc has the shadowing property.

References [Enhancements On Off] (What's this?)

  • [1] D. V. Anosov, On a class of invariant sets for smooth dynamical systems, Proc. Fifth Internat. Conf. on Nonlinear Oscillations, vol. 2, Math. Inst. Ukrainian Acad. Sci., Kiev, 1970, pp. 39-45. (Russian)
  • [2] M. Barge and R. Swanson, Rotation shadowing properties of circle and annulus maps, Ergodic Theory Dynamical Systems 8 (1988), 509-521. MR 980794 (90f:58107)
  • [3] -, Pseudo-orbits and topological entropy, Proc. Amer. Math. Soc., Vol. 109, No. 2 (1990), 559-566. MR 1012923 (90i:58086)
  • [4] M. L. Blank, Metric properties of $ \varepsilon $-trajectories of dynamical systems with stochastic behaviour, Ergodic Theory Dynamical Systems 8 (1988), 365-378. MR 961736 (90b:58143)
  • [5] R. Bowen, On axiom A diffeomorphisms, CBMS Reg. Conf. Ser. Math., vol. 35, Amer. Math. Soc., Providence, RI, 1978. MR 0482842 (58:2888)
  • [6] A. Boyarski and P. Góra, The pseudo-orbit shadowing property for Markov operators in the space of probability density functions, preprint, October 1989.
  • [7] L. Chen, Linking and the shadowing property for piecewise monotone maps, Proc. Amer. Math. Soc. Vol. 113, No. 1 (1991), 251-263. MR 1079695 (92b:58166)
  • [8] -, On the shadowing property for nondegenerated zero entropy piecewise monotone maps, SUNY Stony Brook preprint series, #1990/9, 1990.
  • [9] E. M. Coven, I. Kan, and J. A. Yorke, Pseudo-orbit shadowing in the family of tent maps, Trans. Amer. Math. Soc. 308 (1988), 227-241. MR 946440 (90b:58236)
  • [10] J. E. Franke and J. F. Selgrade, Hyperbolicity and chain recurrence, J. Differential Equations 26 (1977), 27-36. MR 0467834 (57:7685)
  • [11] T. Gedeon and M. Kuchta, Shadowing property of continuous maps, preprint. MR 1086325 (92h:58123)
  • [12] G. W. Henderson, The pseudo-arc as an inverse limit with one binding map, Duke Math. J. 31 (1964), 421-425. MR 0166766 (29:4039)
  • [13] I. Kan, Shadowing properties of quadratic maps, preprint.
  • [14] M. Komuro, The pseudo orbit tracing properties on the space of probability measures, Tokyo J. Math. 7 (1984), 461-468. MR 776950 (86h:54049)
  • [15] S. H. Li, The dynamical properties of the shift maps on the inverse limit space, to appear in Ergod. Th. & Dynam. Sys. MR 1112809
  • [16] P. Walters, On the pseudo-orbit tracing property and its relationship to stability, Lecture Notes in Math., vol. 668, Springer-Verlag, Berlin, Heidelbery, pp. 191-210. MR 518563 (80d:58055)
  • [17] R. F. Williams, One-dimensional nonwandering sets, Topology 6 (1967), 473-487. MR 0217808 (36:897)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F10, 28D05, 54H20, 58F08

Retrieve articles in all journals with MSC: 58F10, 28D05, 54H20, 58F08

Additional Information

Keywords: Shadowing property, inverse limit space, shift map, pseudoarc
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society