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Dense area-preserving homeomorphisms have zero Lyapunov exponents
On isotopy and unimodal inverse limit spaces
1. | Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom |
2. | Department of Mathematics, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia |
References:
[1] |
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.
doi: 10.1090/S0002-9939-96-03690-8. |
[2] |
M. Barge, H. Bruin and S. Štimac, The Ingram conjecture, preprint, 2009, arXiv:0912.4645. |
[3] |
L. Block, S. Jakimovik, J. Keesling and L. Kailhofer, On the classification of inverse limits of tent maps, Fund. Math., 187 (2005), 171-192.
doi: 10.4064/fm187-2-5. |
[4] |
L. Block, J. Keesling, B. Raines and S. Štimac, Homeomorphisms of unimodal inverse limit spaces with non-recurrent critical point, Topology Appl., 156 (2009), 2417-2425.
doi: 10.1016/j.topol.2009.06.006. |
[5] |
K. Brucks and H. Bruin, Subcontinua of inverse limit spaces of unimodal maps, Fund. Math., 160 (1999), 219-246. |
[6] |
K. Brucks and B. Diamond, A symbolic representation of inverse limit spaces for a class of unimodal maps, in "Continua" (Cincinnati, OH, 1994), 207-226, Lect. Notes in Pure and Appl. Math. 170, Dekker, New York, 1995. |
[7] |
K. Brucks and M. Misiurewicz, The trajectory of the turning point is dense for almost all tent maps, Ergod. Th. and Dyn. Sys., 16 (1996), 1173-1183.
doi: 10.1017/S0143385700009962. |
[8] |
H. Bruin, Subcontinua of Fibonacci-like unimodal inverse limit spaces, Topology Proceedings, 31 (2007), 37-50. |
[9] |
L. Kailhofer, A classification of inverse limit spaces of tent maps with periodic critical points, Fund. Math., 177 (2003), 95-120.
doi: 10.4064/fm177-2-1. |
[10] |
B. Raines, Inhomogeneities in non-hyperbolic one-dimensional invariant sets, Fund. Math., 182 (2004), 241-268.
doi: 10.4064/fm182-3-4. |
[11] |
B. Raines and S. Štimac, A classification of inverse limit spaces of tent maps with nonrecurrent critical point, Algebraic and Geometric Topology, 9 (2009), 1049-1088.
doi: 10.2140/agt.2009.9.1049. |
[12] |
S. Štimac, A classification of inverse limit spaces of tent maps with finite critical orbit, Topology Appl., 154 (2007), 2265-2281. |
show all references
References:
[1] |
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.
doi: 10.1090/S0002-9939-96-03690-8. |
[2] |
M. Barge, H. Bruin and S. Štimac, The Ingram conjecture, preprint, 2009, arXiv:0912.4645. |
[3] |
L. Block, S. Jakimovik, J. Keesling and L. Kailhofer, On the classification of inverse limits of tent maps, Fund. Math., 187 (2005), 171-192.
doi: 10.4064/fm187-2-5. |
[4] |
L. Block, J. Keesling, B. Raines and S. Štimac, Homeomorphisms of unimodal inverse limit spaces with non-recurrent critical point, Topology Appl., 156 (2009), 2417-2425.
doi: 10.1016/j.topol.2009.06.006. |
[5] |
K. Brucks and H. Bruin, Subcontinua of inverse limit spaces of unimodal maps, Fund. Math., 160 (1999), 219-246. |
[6] |
K. Brucks and B. Diamond, A symbolic representation of inverse limit spaces for a class of unimodal maps, in "Continua" (Cincinnati, OH, 1994), 207-226, Lect. Notes in Pure and Appl. Math. 170, Dekker, New York, 1995. |
[7] |
K. Brucks and M. Misiurewicz, The trajectory of the turning point is dense for almost all tent maps, Ergod. Th. and Dyn. Sys., 16 (1996), 1173-1183.
doi: 10.1017/S0143385700009962. |
[8] |
H. Bruin, Subcontinua of Fibonacci-like unimodal inverse limit spaces, Topology Proceedings, 31 (2007), 37-50. |
[9] |
L. Kailhofer, A classification of inverse limit spaces of tent maps with periodic critical points, Fund. Math., 177 (2003), 95-120.
doi: 10.4064/fm177-2-1. |
[10] |
B. Raines, Inhomogeneities in non-hyperbolic one-dimensional invariant sets, Fund. Math., 182 (2004), 241-268.
doi: 10.4064/fm182-3-4. |
[11] |
B. Raines and S. Štimac, A classification of inverse limit spaces of tent maps with nonrecurrent critical point, Algebraic and Geometric Topology, 9 (2009), 1049-1088.
doi: 10.2140/agt.2009.9.1049. |
[12] |
S. Štimac, A classification of inverse limit spaces of tent maps with finite critical orbit, Topology Appl., 154 (2007), 2265-2281. |
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