Subcontinua of inverse limit spaces of unimodal maps

Fundamenta Mathematicae

Volumn 160, Issue 3, 1999, Pages 219-246

  Brucks, Karen ^a   Bruin, Henk ^b  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039530515     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. J. M. Aarts and R. J. Fokkink, The classification of solenoids, Proc. Amer. Math. Soc. 111 (1991), 1161-1163.
2. M. Barge, Horseshoe maps and inverse limits, Pacific J. Math. 121 (1986), 29-39.
3. 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.
4. M. Barge and B. Diamond, Homeomorphisms of inverse limit spaces of one-dimensional maps, Fund. Math. 146 (1995), 171-187.
5. _, _, Inverse limit spaces of infinitely renormalizable maps, Topology Appl. 83 (1998), 103-108.
6. _, _, Subcontinua of the closure of the unstable manifold at a homoclinic tangency, Ergodic Theory Dynam. Systems 19 (1999), 1-19.
7. M. Barge and S. Holte, Nearly one-dimensional Hénon attractors and inverse limits, Nonlinearity 8 (1995), 29-42.
8. M. Barge and J. Martin, Endpoints of inverse limit spaces and dynamics, in: Continua with the Houston Problem Book (Cincinnati, OH, 1994), Lecture Notes in Pure and Appl. Math. 170, Dekker, New York, 1995, 165-182.
9. M. Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478-483.
10. K. Brucks, B. Diamond, M. V. Otero-Espinar and C. Tresser, Dense orbits of critical points for the tent map, in: Contemp. Math. 117, Amer. Math. Soc., Providence, RI, 1991, 57-61.
11. H. Bruin, Invariant measures of interval maps, Ph.D. thesis, Delft, 1994.
12. _, Combinatorics of the kneading map, Internat J. Bifur. and Chaos Appl. Sci. Engrg. 5 (1995), 1339-1349.
13. _, Planar embeddings of inverse limit spaces of unimodal maps, Topology Appl., to appear.
14. _, Inverse limit spaces of post-critically finite tent maps, preprint, 1998.
15. W. Dȩbski, On topological types of the simplest indecomposable continua, Colloq. Math. 49 (1985), 203-211.
16. F. Hofbauer, The topological entropy of the transformation x → ax(1 - x), Monatsh. Math. 90 (1980), 117-141.
17. F. Hofbauer and G. Keller, Quadratic maps without asymptotic measure, Comm. Math. Phys. 127 (1990), 319-337.
18. S. Holte, Generalized horseshoe maps and inverse limits, Pacific J. Math. 156 (1992), 297-305.
19. W. de Melo and S. van Strien, One-Dimensional Dynamics, Springer, New York, 1993.
20. J. Mioduszewski, Mappings of inverse limits, Colloq. Math. 10 (1963), 39-44.
21. S. Nadler, Continuum Theory, Dekker, New York, 1992.
22. R. C. Swanson and H. W. Volkmer, Invariants of weak equivalence in primitive matrices, preprint, 1998.
23. W. T. Watkins, Homeomorphic classification of certain inverse limit spaces with open bonding maps, Pacific J. Math. 103 (1982), 589-601.
24. R. F. Williams, One-dimensional nonwandering sets, Topology 6 (1967), 473-487.