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Volume 9, issue 2 (2009)

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A classification of inverse limit spaces of tent maps with a nonrecurrent critical point

Brian E Raines and Sonja Štimac

Algebraic & Geometric Topology 9 (2009) 1049–1088
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 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, The dynamics of continuous maps of finite graphs through inverse limits, Trans. Amer. Math. Soc. 344 (1994) 773 MR1236222
4 M Barge, B Diamond, Homeomorphisms of inverse limit spaces of one-dimensional maps, Fund. Math. 146 (1995) 171 MR1314982
5 M Barge, B Diamond, A complete invariant for the topology of one-dimensional substitution tiling spaces, Ergodic Theory Dynam. Systems 21 (2001) 1333 MR1855835
6 M Barge, J Jacklitch, G Vago, Homeomorphisms of one-dimensional inverse limits with applications to substitution tilings, unstable manifolds, and tent maps, from: "Geometry and topology in dynamics (Winston-Salem, NC, 1998/San Antonio, TX, 1999)" (editors M Barge, K Kuperberg), Contemp. Math. 246, Amer. Math. Soc. (1999) 1 MR1732368
7 M Barge, J Martin, Chaos, periodicity, and snakelike continua, Trans. Amer. Math. Soc. 289 (1985) 355 MR779069
8 M Barge, J Martin, The construction of global attractors, Proc. Amer. Math. Soc. 110 (1990) 523 MR1023342
9 M Barge, J Martin, Endpoints of inverse limit spaces and dynamics, from: "Continua (Cincinnati, OH, 1994)" (editors H Cook, W T Ingram, K T Kuperberg, A Lelek, P Minc), Lecture Notes in Pure and Appl. Math. 170, Dekker (1995) 165 MR1326840
10 L Block, S Jakimovik, L Kailhofer, J Keesling, On the classification of inverse limits of tent maps, Fund. Math. 187 (2005) 171 MR2214878
11 K Brucks, H Bruin, Subcontinua of inverse limit spaces of unimodal maps, Fund. Math. 160 (1999) 219 MR1708988
12 K M Brucks, B Diamond, A symbolic representation of inverse limit spaces for a class of unimodal maps, from: "Continua (Cincinnati, OH, 1994)" (editors H Cook, W T Ingram, K T Kuperberg, A Lelek, P Minc), Lecture Notes in Pure and Appl. Math. 170, Dekker (1995) 207 MR1326844
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 P Collet, J P Eckmann, Iterated maps on the interval as dynamical systems, 1, Birkhäuser (1980) MR613981
17 C Good, R Knight, B E Raines, Nonhyperbolic one-dimensional invariant sets with a countably infinite collection of inhomogeneities, Fund. Math. 192 (2006) 267 MR2278390
18 C Good, B E Raines, Continuum many tent map inverse limits with homeomorphic postcritical ω–limit sets, Fund. Math. 191 (2006) 1 MR2232193
19 L Kailhofer, A partial classification of inverse limit spaces of tent maps with periodic critical points, Topology Appl. 123 (2002) 235 MR1918499
20 L Kailhofer, A classification of inverse limit spaces of tent maps with periodic critical points, Fund. Math. 177 (2003) 95 MR1992527
21 J Kennedy, D R Stockman, J A Yorke, Inverse limits and models with backward dynamics, to appear in Journal Math. Econ.
22 J Kennedy, D R Stockman, J A Yorke, Inverse limits and an implicitly defined difference equation from economics, Topology Appl. 154 (2007) 2533 MR2332869
23 A Medio, B E Raines, Inverse limit spaces arising from problems in economics, Topology Appl. 153 (2006) 3437 MR2270597
24 A Medio, B E Raines, Backward dynamics in economics. The inverse limit approach, J. Econom. Dynam. Control 31 (2007) 1633 MR2317572
25 B E Raines, Inhomogeneities in non-hyperbolic one-dimensional invariant sets, Fund. Math. 182 (2004) 241 MR2098780
26 B E Raines, S Štimac, Structure of inverse limit spaces of tent maps with nonrecurrent critical points, Glas. Mat. Ser. III 42(62) (2007) 43 MR2332656
27 S Štimac, Topological classification of Knaster continua with finitely many endpoints (Croatian), PhD thesis, University of Zagreb (2002)
28 S Štimac, Structure of inverse limit spaces of tent maps with finite critical orbit, Fund. Math. 191 (2006) 125 MR2231059
29 S Štimac, A classification of inverse limit spaces of tent maps with finite critical orbit, Topology Appl. 154 (2007) 2265 MR2328011
30 R Swanson, H Volkmer, Invariants of weak equivalence in primitive matrices, Ergodic Theory Dynam. Systems 20 (2000) 611 MR1756989