Inhomogeneities in non-hyperbolic one-dimensional invariant sets

Fundamenta Mathematicae

Volumn 182, Issue 3, 2004, Pages 241-268

  Raines, Brian E ^a,b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b BAYLOR UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10244277005     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm182-3-4     Document Type: Article

References (23)

1. J. E. Anderson and I. F. Putnam, Topological invariants for substitution tilings and their associated C* -algebras, Ergodic Theory Dynam. Systems 18 (1998), 509-537.
2. M. Barge, K. Brucks and B. Diamond, Self-similarity in inverse limit spaces of the tent family, Proc. Amer. Math. Soc. 124 (1996), 3563-3570.
3. M. Barge and B. Diamond, A complete invariant for the topology of one-dimensional substitution tiling spaces, Ergodic Theory Dynam. Systems 21 (2001), 1333-1358.
4. M. Barge and S. Holte, Nearly one-dimensional Hénon attractors and inverse limits, Nonlinearity 8 (1995), 29-42.
5. M. Barge and J. Martin, Chaos, periodicity, and snakelike continua, Trans. Amer. Math. Soc. 289 (1985), 355-365.
6. _, _, The construction of global attractors, Proc. Amer. Math. Soc. 110 (1990), 523-525.
7. _, _, Endpoints of inverse limit spaces and dynamics, in: Continua (Cincinnati, OH, 1994), Dekker, New York, 1995, 165-182.
8. L. S. Block and W. A. Coppel, Dynamics in One Dimension, Springer, Berlin, 1992.
9. H. Bruin, Planar embeddings of inverse limit spaces of unimodal maps, Topology Appl. 96 (1999), 191-208.
10. _, Inverse limit spaces of post-critically finite tent maps, Fund. Math. 165 (2000), 125-138.
11. P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser Boston, 1980.
12. W. de Melo and S. van Strien, One-Dimensional Dynamics, Ergeb. Math. Grenzgeb. 25, Springer, Berlin, 1993.
13. J. G. Hocking and G. S. Young, Topology, 2nd ed., Dover Publ., New York, 1988.
14. W. T. Ingram, An atriodic tree-like continuum with positive span, Fund. Math. 77 (1972), 99-107.
15. _, Inverse Limits, Soc. Mat. Mexicana, Mexico, 2000.
16. A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, New York, 1995.
17. B. Raines, One-dimensional dynamics and inverse limits, D.Phil, thesis, Oxford Univ., 2002.
18. _, Inverse limits of tent maps without the pseudo-orbit shadowing property, Topology Proc. 27 (2003), 1-9.
19. J. van Mill and G. M. Reed (eds.), Open Problems in Topology, North-Holland, Amsterdam, 1990.
20. R. F. Williams, One-dimensional non-wandering sets, Topology 6 (1967), 473-487.
21. _, Classification of one dimensional attractors, in: Global Analysis (Berkeley, CA, 1968), Proc. Sympos. Pure Math. 14, Amer. Math. Soc., Providence, RI, 1970, 341-361
22. _, The "DA" maps of Smale and structural stability, in: Global Analysis (Berkeley, CA, 1968), Proc. Sympos. Pure Math. 14, Amer. Math. Soc., Providence, RI, 1970, 329-334.
23. I. Yi, Canonical symbolic dynamics for one-dimensional generalized solenoids, Trans. Amer. Math. Soc. 353 (2001), 3741-3767.