Publications
2021
Limits of sequences of pseudo-Anosov maps and of hyperbolic 3–manifolds
Bonnot, S., de Carvalho, A., González-Meneses, J., & Hall, T. (2021). Limits of sequences of pseudo-Anosov maps andof hyperbolic 3–manifolds. Algebraic & Geometric Topology, 21(3), 1351-1370. doi:10.2140/agt.2021.21.1351
Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries
Boyland, P., Carvalho, A. D., & Hall, T. (2017). Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries. Geom. Topol., 25, 111-228. Retrieved from http://dx.doi.org/10.2140/gt.2021.25.111
2020
Statistical Stability for Barge-Martin Attractors Derived from Tent Maps
Hall, T., Boyland, P., & de Carvalho, A. (2020). Statistical Stability for Barge-Martin Attractors Derived from Tent Maps. Discrete and Continuous Dynamical Systems Series A. Retrieved from https://arxiv.org/abs/1812.00453
Typical path components in tent map inverse limits
Boyland, P., de Carvalho, A., & Hall, T. (n.d.). Typical path components in tent map inverse limits. Fundamenta Mathematicae, 250, 301-318. doi:10.4064/fm810-1-2020
2018
INTERSECTIONS OF MULTICURVES FROM DYNNIKOV COORDINATES
YURTTAŞ, S. Ö., & HALL, T. (2018). INTERSECTIONS OF MULTICURVES FROM DYNNIKOV COORDINATES. Bulletin of the Australian Mathematical Society, 98(1), 149-158. doi:10.1017/s0004972718000308
2017
Itineraries for inverse limits of tent maps: A backward view
Boyland, P., de Carvalho, A., & Hall, T. (2017). Itineraries for inverse limits of tent maps: A backward view. Topology and its Applications, 232, 1-12. doi:10.1016/j.topol.2017.09.012
Counting components of an integral lamination
Yurttaş, S. Ö., & Hall, T. (2017). Counting components of an integral lamination. manuscripta mathematica, 153(1-2), 263-278. doi:10.1007/s00229-016-0885-4
2016
On digit frequencies in beta-expansions
Boyland, P., de Carvalho, A., & Hall, T. (2016). On digit frequencies in beta-expansions. Transactions of the American Mathematical Society (TRAN), 368(12), 8633-8674. doi:10.1090/tran/6617
New rotation sets in a family of torus homeomorphisms
Boyland, P., de Carvalho, A., & Hall, T. (2016). New rotation sets in a family of torus homeomorphisms. Inventiones Mathematicae, 204(3), 895-937. doi:10.1007/s00222-015-0628-2
2015
Symbol ratio minimax sequences in the lexicographic order
Boyland, P., de Carvalho, A., & Hall, T. (2015). Symbol ratio minimax sequences in the lexicographic order. Ergodic Theory and Dynamical Systems, 35(8), 2371-2396. doi:10.1017/etds.2014.44
2014
Riemann surfaces out of paper
de Carvalho, A., & Hall, T. (2014). Riemann surfaces out of paper. Proceedings of the London Mathematical Society, 108(3), 541-574. doi:10.1112/plms/pdt020
2013
Inverse limits as attractors in parameterized families
Boyland, P., de Carvalho, A., & Hall, T. (2013). Inverse limits as attractors in parameterized families. Bulletin of the London Mathematical Society, 45(5), 1075-1085. doi:10.1112/blms/bdt032
2012
Paper folding, Riemann surfaces and convergence of pseudo-Anosov sequences
de Carvalho, A., & Hall, T. (2012). Paper folding, Riemann surfaces and convergence of pseudo-Anosov sequences. Geometry & Topology, 16(4), 1881-1966. doi:10.2140/gt.2012.16.1881
2010
Paper surfaces and dynamical limits.
de Carvalho, A., & Hall, T. (2010). Paper surfaces and dynamical limits.. Proceedings of the National Academy of Sciences of the United States of America, 107(32), 14030-14035. doi:10.1073/pnas.1001947107
Decoration invariants for horseshoe braids
de Carvalho, A., & Hall, T. (2010). Decoration invariants for horseshoe braids. Discrete & Continuous Dynamical Systems - A, 27(3), 863-906. doi:10.3934/dcds.2010.27.863
Kneading Theory
Hall, T. (2010). Kneading Theory. Scholarpedia, 5(11), 3956. Retrieved from http://www.scholarpedia.org/article/Kneading_theory
2009
On the topological entropy of families of braids
Hall, T., & Yurttaş, S. Ö. (2009). On the topological entropy of families of braids. Topology and its Applications, 156(8), 1554-1564. doi:10.1016/j.topol.2009.01.005
On period minimal pseudo-Anosov braids
de Carvalho, A., Hall, T., & Venzke, R. (n.d.). On period minimal pseudo-Anosov braids. Proceedings of the American Mathematical Society, 137(5), 1771-1776. doi:10.1090/s0002-9939-08-09709-8
2008
Topology of chaotic mixing patterns.
Thiffeault, J. -L., Finn, M. D., Gouillart, E., & Hall, T. (2008). Topology of chaotic mixing patterns.. Chaos (Woodbury, N.Y.), 18(3), 033123. doi:10.1063/1.2973815
2004
Unimodal generalized pseudo-Anosov maps
de Carvalho, A., & Hall, T. (2004). Unimodal generalized pseudo-Anosov maps. Geometry & Topology, 8(3), 1127-1188. doi:10.2140/gt.2004.8.1127
Braid forcing and star-shaped train tracks
de Carvalho, A., & Hall, T. (2004). Braid forcing and star-shaped train tracks. Topology, 43(2), 247-287. doi:10.1016/s0040-9383(03)00042-9
2003
Conjugacies between horseshoe braids
Carvalho, A. D., & Hall, T. (2003). Conjugacies between horseshoe braids. Nonlinearity, 16(4), 1329-1338. doi:10.1088/0951-7715/16/4/308
Symbolic dynamics and topological models in dimensions 1 and 2
de Carvalho, A., & Hall, T. (2003). Symbolic dynamics and topological models in dimensions 1 and 2. In S. Bezuglyi, & S. Kolyada (Eds.), Dynamical systems and Ergodic theory Vol. 310 (pp. 40-59). Cambridge: Cambridge University Press.
2002
How to prune a horseshoe
Carvalho, A. D., & Hall, T. (2002). How to prune a horseshoe. Nonlinearity, 15(3), R19-R68. doi:10.1088/0951-7715/15/3/201
The Forcing Relation for Horseshoe Braid Types
Carvalho, A. D., & Hall, T. (2002). The Forcing Relation for Horseshoe Braid Types. Experimental Mathematics, 11(2), 271-288. doi:10.1080/10586458.2002.10504691
2001
Pruning theory and Thurston's classification of surface homeomorphisms
de Carvalho, A., & Hall, T. (2001). Pruning theory and Thurston's classification of surface homeomorphisms. Journal of the European Mathematical Society, 3(4), 287-333. doi:10.1007/s100970100034
1999
Isotopy Stable Dynamics Relative to Compact Invariant Sets
Boyland, P., & Hall, T. (1999). Isotopy Stable Dynamics Relative to Compact Invariant Sets. Proceedings of the London Mathematical Society, 79(3), 673-693. doi:10.1112/s0024611599012009
1996
Zeros of the kneading invariant and topological entropy for Lorenz maps
Hall, T. D. H., & Glendinning, P. (1996). Zeros of the kneading invariant and topological entropy for Lorenz maps. Nonlinearity, 9(4), 999-1014.
1994
Period-multiplying cascades for diffeomorphisms of the disc
Gambaudo, J. -M., Guaschi, J., & Hall, T. (1994). Period-multiplying cascades for diffeomorphisms of the disc. Mathematical Proceedings of the Cambridge Philosophical Society, 116(2), 359-374. doi:10.1017/s0305004100072649
The creation of horseshoes
Hall, T. (1994). The creation of horseshoes. Nonlinearity, 7(3), 861-924. doi:10.1088/0951-7715/7/3/008
Fat one-dimensional representatives of pseudo-Anosov isotopy classes with minimal periodic orbit structure
Hall, T. (1994). Fat one-dimensional representatives of pseudo-Anosov isotopy classes with minimal periodic orbit structure. Nonlinearity, 7(2), 367-384. doi:10.1088/0951-7715/7/2/004
1993
Weak universality in two-dimensional transitions to chaos.
Hall, T. (1993). Weak universality in two-dimensional transitions to chaos.. Physical review letters, 71(1), 58-61. doi:10.1103/physrevlett.71.58
L'ensemble de rotation des homéomorphismes pseudo-Anosov
Hall, T. D. H., Guaschi, J., & Gambaudo, J. -M. (1993). L'ensemble de rotation des homéomorphismes pseudo-Anosov. C.R. Acad. Sci. Paris Ser. I Math..
1991
Unremovable periodic orbits of homeomorphisms
Hall, T. (1991). Unremovable periodic orbits of homeomorphisms. Mathematical Proceedings of the Cambridge Philosophical Society, 110(3), 523-531. doi:10.1017/s0305004100070596