Volume 16, issue 4 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
The Ingram conjecture

Marcy Barge, Henk Bruin and Sonja Štimac

Geometry & Topology 16 (2012) 2481–2516
Bibliography
1 J E Anderson, I F Putnam, Topological invariants for substitution tilings and their associated $C^{*}$–algebras, Ergodic Theory Dynam. Systems 18 (1998) 509 MR1631708
2 M Barge, K M Brucks, B Diamond, Self-similarity in inverse limit spaces of the tent family, Proc. Amer. Math. Soc. 124 (1996) 3563 MR1363409
3 M Barge, B Diamond, Homeomorphisms of inverse limit spaces of one-dimensional maps, Fund. Math. 146 (1995) 171 MR1314982
4 M Barge, B Diamond, Inverse limit spaces of infinitely renormalizable maps, Topology Appl. 83 (1998) 103 MR1604798
5 M Barge, B Diamond, Subcontinua of the closure of the unstable manifold at a homoclinic tangency, Ergodic Theory Dynam. Systems 19 (1999) 289 MR1685395
6 M Barge, S Holte, Nearly one-dimensional Hénon attractors and inverse limits, Nonlinearity 8 (1995) 29 MR1313141
7 M Barge, W T Ingram, Inverse limits on $[0,1]$ using logistic bonding maps, Topology Appl. 72 (1996) 159 MR1404274
8 L Block, S Jakimovik, L Kailhofer, J Keesling, On the classification of inverse limits of tent maps, Fund. Math. 187 (2005) 171 MR2214878
9 L Block, S Jakimovik, J Keesling, On Ingram's conjecture, Topology Proc. 30 (2006) 95 MR2280661
10 L Block, J Keesling, B E Raines, S Štimac, Homeomorphisms of unimodal inverse limit spaces with a non-recurrent critical point, Topology Appl. 156 (2009) 2417 MR2546944
11 K M Brucks, H Bruin, Subcontinua of inverse limit spaces of unimodal maps, Fund. Math. 160 (1999) 219 MR1708988
12 K M Brucks, B Diamond, Monotonicity of auto-expansions, Phys. D 51 (1991) 39 MR1128801
13 H Bruin, Planar embeddings of inverse limit spaces of unimodal maps, Topology Appl. 96 (1999) 191 MR1709688
14 H Bruin, Inverse limit spaces of post-critically finite tent maps, Fund. Math. 165 (2000) 125 MR1808727
15 H Bruin, Subcontinua of Fibonacci-like inverse limit spaces, Topology Proc. 31 (2007) 37 MR2363150
16 A Douady, Topological entropy of unimodal maps: monotonicity for quadratic polynomials, from: "Real and complex dynamical systems" (editors B Branner, P Hjorth), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Kluwer Acad. Publ. (1995) 65
17 M J Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Statist. Phys. 19 (1978) 25 MR0501179
18 J Graczyk, G Światek, Generic hyperbolicity in the logistic family, Ann. of Math. 146 (1997) 1 MR1469316
19 J Guckenheimer, Sensitive dependence to initial conditions for one-dimensional maps, Comm. Math. Phys. 70 (1979) 133 MR553966
20 F Hofbauer, P Raith, K Simon, Hausdorff dimension for some hyperbolic attractors with overlaps and without finite Markov partition, Ergodic Theory Dynam. Systems 27 (2007) 1143 MR2342970
21 W T Ingram, Inverse limits on $[0,1]$ using tent maps and certain other piecewise linear bonding maps, from: "Continua" (editors H Cook, W T Ingram, K T Kuperberg, A Lelek, P Minc), Lecture Notes in Pure and Appl. Math. 170, Dekker (1995) 253 MR1326847
22 L Kailhofer, A classification of inverse limit spaces of tent maps with periodic critical points, Fund. Math. 177 (2003) 95 MR1992527
23 M Lyubich, Dynamics of quadratic polynomials. I, II, Acta Math. 178 (1997) 185, 247 MR1459261
24 W de Melo, S van Strien, One-dimensional dynamics, Ergeb. Math. Grenzgeb. 25, Springer (1993) MR1239171
25 J Milnor, W Thurston, On iterated maps of the interval, from: "Dynamical systems" (editor J C Alexander), Lecture Notes in Math. 1342, Springer (1988) 465 MR970571
26 M Misiurewicz, Embedding inverse limits of interval maps as attractors, Fund. Math. 125 (1985) 23 MR813986
27 M Misiurewicz, W Szlenk, Entropy of piecewise monotone mappings, Studia Math. 67 (1980) 45 MR579440
28 B E Raines, Inhomogeneities in non-hyperbolic one-dimensional invariant sets, Fund. Math. 182 (2004) 241 MR2098780
29 B E Raines, S Štimac, A classification of inverse limit spaces of tent maps with a nonrecurrent critical point, Algebr. Geom. Topol. 9 (2009) 1049 MR2511139
30 D Singer, Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math. 35 (1978) 260 MR0494306
31 S Štimac, A classification of inverse limit spaces of tent maps with finite critical orbit, Topology Appl. 154 (2007) 2265 MR2328011
32 R Swanson, H Volkmer, Invariants of weak equivalence in primitive matrices, Ergodic Theory Dynam. Systems 20 (2000) 611 MR1756989
33 W Szczechla, Inverse limits of certain interval mappings as attractors in two dimensions, Fund. Math. 133 (1989) 1 MR1059158
34 C Tresser, P Coullet, Itérations d'endomorphismes et groupe de renormalisation, C. R. Acad. Sci. Paris Sér. A-B 287 (1978) MR512110
35 R F Williams, One-dimensional non-wandering sets, Topology 6 (1967) 473 MR0217808
36 R F Williams, Classification of one dimensional attractors, from: "Global Analysis", Proc. Symp. Pure Math. 14, Amer. Math. Soc. (1970) 341 MR0266227