Publications/Preprints of Henk Bruin

    1992

  1. Numerical determination of the continued fraction expansion of the rotation number, Physica D 59 (1992) 158-168.
  2. 1994

  3. Topological conditions for the existence of invariant measures for unimodal maps, Ergod. Th. and Dyn. Sys. 14 (1994) 433-451. [.pdf]
  4. 1995

  5. Induced maps, Markov extensions and invariant measures in one-dimensional dynamics, Commun. Math. Phys. 168 (1995) 571-580. [.pdf] The original publication is available at [http://www.springerlink.com]
  6. Combinatorics of the kneading map, Int. Jour. of Bifur. and Chaos 5 (1995) 1339-1349. [.pdf]
  7. Non-monotonicity of entropy of interval maps, Phys. Lett. A 202 (1995) 359-362. Preprint version [.pdf]
  8. 1996

  9. (with Gerhard Keller, Tomasz Nowicki, Sebastian van Strien) Wild Cantor attractors exist, Annals of Math. 143 (1996) 97-130. [.pdf]
  10. Quasi-symmetry of conjugacies between interval maps, Nonlinearity 9 (1996) 1191-1207. [.pdf]
  11. An algorithm to compute the topological entropy of a unimodal map, Proceedings contribution for the conference in memory of W. Szlenk, Barcelona (1996) Internat. J. Bifur. Chaos 9 (1999) 1881-1882. [.pdf]

    1997

  12. (with Gerhard Keller and Matthias St. Pierre) Adding machines and wild attractors, Ergod. Th. and Dyn. Sys. 17 (1997) 1267-1287. [.pdf]
  13. 1998

  14. Topological conditions for the existence of Cantor attractors, Trans. Amer. Math. Soc. 350 (1998) 2229-2263. [.pdf]
  15. For almost every tent-map, the turning point is typical, Fund. Math. 155 (1998) 215-235; [.pdf]
  16. The existence of absolutely continuous invariant measures is not a topological invariant for unimodal maps, Ergod. Th.and Dyn. Sys. 18 (1998) 555-565. [.pdf]
  17. (with Gerhard Keller) Equilibrium states for unimodal maps, Ergod. Th. and Dyn. Sys. 18 (1998) 765-789. [.pdf]
  18. (with Jane Hawkins) Examples of expanding C1 maps having no sigma-finite invariant measure equivalent to Lebesgue, Isr. J. Math. 108 (1998) 83-107. [.pdf]
  19. 1999

  20. (with Karen M. Brucks) Subcontinua of inverse limit spaces of unimodal maps, Fund. Math. 160 (1999) 219-246. [.pdf]
  21. Homeomorphic restrictions of unimodal maps, Contemp. Math. 246 (1999) 47-56; [.pdf]
  22. Planar embeddings of inverse limit spaces of unimodal maps. Topology and its Applications 96 (1999) 191-208. [.pdf]
  23. 2000

  24. Inverse limit spaces of post-critically finite tent maps. Fund. Math. 165 (2000) 125-138 [.pdf]
  25. Dimensions of recurrence times and minimal subshifts, Conference Proceedings: from Chrystal to Chaos, Luminy (2000), [.pdf]
  26. 2001

  27. (with Jane Hawkins) Exactness and maximal automorphic factors of unimodal maps, Ergod. Th. and Dyn. Sys. 21 (2001) 1009-1034; [.pdf]
  28. (with Sebastian van Strien) Existence of acips for multimodal maps, in Global Analysis of Dynamical Systems, Festschrift dedicated to Floris Takens for his 60th birthday (2001) [.pdf]
  29. 2002

  30. (with Dierk Schleicher) Symbolic dynamics of quadratic polynomials. Preprint (2002) This is available on the web-pages of the Mittag-Leffler institute.
  31. 2003

  32. (with Stefano Luzzatto and Sebastian van Strien) Decay of correlations in one-dimensional dynamics, Preprint (1999) and (2001), Ann. Sci. Ec. Norm. Sup. 36 (2003) 621-646. [.pdf]
  33. (with Benoit Saussol, Serge Troubetzkoy and Sandro Vaienti) Return time statistics via inducing, Ergod. Th. and Dyn. Sys. 23 (2003) 991-1013; [.pdf]
  34. (with Sebastian van Strien) Expansion of derivatives in one-dimensional dynamics, Isr. J. Math. 137 (2003) 223-263. [.pdf]
  35. (with Sergiy Kolyada and L'ubomir Snoha) Minimal nonhomogeneous continua, Colloq. Math. 95 (2003) 123-132. [.pdf]
  36. (with Sandro Vaienti) Return time statistics for unimodal maps. Fund. Math. 176 (2003) 77--94. [.pdf]
  37. Minimal Cantor systems and unimodal maps. J. Difference Eq. and Appl. 9 (2003) 305--318. [.pdf]
  38. (with Serge Troubetzkoy) The Gauss map on a class of interval translation mappings. Isr. J. Math. 137 (2003) 125-148. [.pdf]
  39. (with Andre Lambert, Guillaume Poggiaspalla and Sandro Vaienti) Numerical analysis for a discontinuous rotation of the torus. Chaos 13 (2003) 558-571. The original publication is available at [http://www.springerlink.com]
  40. (with Weixiao Shen and Sebastian van Strien) Invariant measures exist without a growth condition. Commun. Math. Phys. 241 (2003) 287-306 [.pdf].
    The original publication is available at [http://www.springerlink.com]
  41. 2004

  42. (with Martijn van Noort) Nonconformal perturbations of z -> z 2 + c: the 1:3 resonance, Nonlinearity 17 (2004) 765 - 789 [.pdf]
  43. 2005

  44. Asymptotic arc-components of unimodal inverse limit spaces, Top. & Appl. 152 (2005) 182 - 200. [.pdf]
  45. (with Karen Brucks) Topics from one-dimensional dynamics, London Mathematical Society, Student Texts 62 Cambridge University Press 2004. Available at Cambridge University Press
  46. (with Mark Holland and Ian Melbourne) Subexponential decay of correlations for compact group extension of nonuniformly expanding systems, Ergod. Th. and Dyn. Sys. 25 (2005) 1719-1738. [.pdf]
  47. (with Mark Holland and Matt Nicol) Livsic regularity for Markov systems, Ergod. Th. and Dyn. Sys. 25 (2005) 1739-1766. [.pdf]
  48. (with Oksana Volkova) The complexity of Fibonacci-like kneading sequences, Theo. Comp. Science. 377 (2005) 379-389. [.pdf]
  49. 2006

  50. (with Weixiao Shen and Sebastian van Strien) Existence of unique SRB-measures is typical for unimodal families, Annales Scientifiques de l'ENS, 4e serie, 39 (2006) 381-414. [.pdf]
  51. (with Stefano Luzzatto) Topological invariance of the sign of the Lyapunov exponents in one-dimensional maps, Proc. Amer. Math. Soc. 134 (2006), no. 1, 265-272 (electronic). In Preprint 2004 version: [.pdf]
  52. (with Mike Todd) Markov extensions and lifting measures for complex polynomials, [.pdf] Ergod. Th. and Dyn. Sys. 27 (2007) 743-768.
  53. Renormalisation in a class of interval translation maps of d branches, Dynamical Systems, an international journal 22 (2007) 11 - 24. Preprint version 2006. [.pdf]
  54. Subcontinua of Fibonacci-like unimodal inverse limit spaces. Topology Proceedings 31 (2007) no. 1, 37-50. [.pdf]
  55. (with Mike Todd) Complex maps without invariant densities, Nonlinearity 19 (2006) 2929-2945. Preprint (Version October 2006). [.pdf]
  56. 2007

  57. (with Mike Todd) Equilibrium states for interval maps: the potential -t log |Df|. Ann. Sci. Ecol Norm. Sup. 42 2009, 559-600. Preprint 2007, Revised version of January 2009: [.pdf]
  58. (with Juan Rivera-Letelier, Weixiao Shen and Sebastian van Strien) Large derivatives, backward contraction and invariant densities for interval maps, Preprint version 2007. [.pdf].
    Inventiones Mathematicae 172 (2008), 509-533. The original publication is available at [http://www.springerlink.com].
  59. (with Jane Hawkins) Rigidity of smooth one-sided Bernoulli endomorphisms, Preprint 2007 - revised 2009, [.pdf] New York Journal of Maths. 15 (2009), 451-483.
  60. Combinatorics of (Fibonacci-like) unimodal maps. Notes used for Spring School at Luminy, April 2006, "Séminaires et Congrès" 20 17-37 (2010). [.pdf]
  61. 2008

  62. (with Jawad Al-Khal and Michael Jakobson) New examples of S-unimodal maps with a sigma-finite absolutely continuous invariant measure, Discrete and Continuous Dynamical Systems, 22 no. 1-2, (2008) 35 - 61, see [here] for journal's version. Earlier preprint version in [.pdf]
  63. (with Mike Todd) Equilibrium states for interval maps: potentials with sup φ - inf φ < h top(f), Commun. Math. Phys. 283 (2008) 579-611. The original publication is available at this Springer site
    Updated version December 2010, [.pdf]
  64. (with Mike Todd) Return time statistics for invariant measures for interval maps with positive Lyapunov exponent. Version August 2008, [.pdf]. Stochastics and Dynamics 9 (2009), 81-100.
  65. (with Michael Jakobson and appendix by Genadi Levin) New examples of topologically equivalent S-unimodal maps with different metric properties, Contemp. Math. 469 2008 119-139. [.pdf]
  66. (with Jonathan Deane) Piecewise contractions are asymptotically periodic, Proc. Amer. Math. Soc. 137 (2009), 1389-1395. [.pdf]
  67. (with Dierk Schleicher) Admissibility of kneading sequences and structure of Hubbard trees for quadratic polynomials. Journal Lond. Math. Soc. 78 (2008), no. 2, 502--522. [.pdf]
  68. (Non)invertibility of Fibonacci-like unimodal maps restricted to their critical omega-limit sets. Preprint 2008. [.pdf], Topology Proceedings 37 (2011) 459-480.
  69. (with Alexandra Kaffl and Dierk Schleicher) Existence of quadratic Hubbard trees. Fund. Math. 202 (2009) 251-279, [.pdf]
  70. (with Mark Demers and Ian Melbourne) Existence and convergence properties of physical measures for certain dynamical systems with holes, Preprint 2008 (revised and extended after the 2007 preprint) [.pdf]
    Ergod. Th. and Dyn. Sys. 30 2010, 687-728 (Published Online by Cambridge University Press 24 Nov 2009 doi:10.1017/S0143385709000200)
  71. 2009

  72. (with Matt Nicol and Dalia Terhesiu) On Young towers associated with infinite measure preserving transformations, Stoch. and Dynamics, 9 (2009), 635 - 655, in [.pdf], see also World Scientific Publishing Company
  73. (with Sebastian van Strien) Monotonicity of entropy for real multimodal maps Preprint 2009, [.pdf]
  74. (with Marcy Barge and Sonja Stimac) The Ingram conjecture Updated preprint version July 2011 [.pdf] to appear in Geometry and Topology.
  75. (with Víctor Jiménez López) On the Lebesgue measure of Li-Yorke pairs for interval maps Preprint 2009, [.pdf] Commun. Math. Phys. 299 (2010), 523--560. The final publication is available at http://www.springerlink.com/content/fu01lpu5u4305572/. (DOI: 10.1007/s00220-010-1085-9)
  76. 2010

  77. (with Marcy Barge, Leslie Jones and Lorenzo Sadun) Homological Pisot substitutions and exact regularity Preprint 2010, [.pdf] Isr. J. Math. 188 2012, 281-300 (DOI) 10.1007/s11856-011-0123-4
  78. (with Sonja Stimac) On isotopy and unimodal inverse limit spaces [.pdf], Discrete and Continuous Dynamical Systems 32 (2012), no. 4, 1245-1253.
  79. (with Renaud Leplaideur) Renormalization, thermodynamic formalism and quasi-crystals in subshifts. Preprint 2010 (updated 2012) [.pdf] to appear in Commun. Math. Phys.

    2011

  80. (with Jozef Bobok) The topological entropy of Banach spaces Preprint 2011 [.pdf] Accepted in the Journal of Difference Equations and Applications where it will appear shortly.
  81. (with Mike Todd) Transience and thermodynamic formalism for infinitely branched interval maps Preprint 2011 [.pdf]. Journal of the London Mathematical Society 86 2012, 171-194 DOI: 10.1112/jlms/jdr081
  82. (with Greg Clack) Inducing and unique ergodicity of double rotations Preprint 2011 [.pdf], Discrete and Continuous Dynamical Systems 32, no. 12 2012. Click here for the electronic version of the journal.

    2012

  83. (with Mike Todd) Wild attractors and thermodynamic formalism, Preprint 2012 [.pdf]
  84. (with Dierk Schleicher) Bernoulli measure of complex admissible kneading sequences, Preprint 2012 [.pdf] to appear in Ergod. Th. Dyn. Sys.
  85. (with Dierk Schleicher) Hausdorff dimension of biaccessible angles for quadratic polynomials, Preprint 2012 [.pdf]

See also MathSciNet
H.Bruin@surrey.ac.uk
Updated June 3 2011