Publications/Preprints of Henk Bruin
1992
-
Numerical determination of the continued fraction expansion of the
rotation number,
Physica D 59 (1992) 158-168.
1994
-
Topological conditions for the existence of invariant measures for
unimodal maps,
Ergod. Th. and Dyn. Sys. 14 (1994) 433-451.
[.pdf]
1995
-
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]
-
Combinatorics of the kneading map,
Int. Jour. of Bifur. and Chaos 5 (1995) 1339-1349.
[.pdf]
-
Non-monotonicity of entropy of interval maps,
Phys. Lett. A 202 (1995) 359-362. Preprint version
[.pdf]
1996
-
(with Gerhard Keller, Tomasz Nowicki, Sebastian van Strien)
Wild Cantor attractors exist,
Annals of Math. 143 (1996) 97-130.
[.pdf]
-
Quasi-symmetry of conjugacies between interval maps,
Nonlinearity 9 (1996) 1191-1207.
[.pdf]
-
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
-
(with Gerhard Keller and Matthias St. Pierre)
Adding machines and wild attractors,
Ergod. Th. and Dyn. Sys. 17 (1997) 1267-1287.
[.pdf]
1998
-
Topological conditions for the existence of Cantor attractors,
Trans. Amer. Math. Soc. 350 (1998) 2229-2263.
[.pdf]
-
For almost every tent-map, the turning point is typical,
Fund. Math. 155 (1998) 215-235;
[.pdf]
-
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]
- (with Gerhard Keller)
Equilibrium states for unimodal maps,
Ergod. Th. and Dyn. Sys. 18 (1998) 765-789.
[.pdf]
- (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]
1999
- (with Karen M. Brucks)
Subcontinua of inverse limit spaces of unimodal maps,
Fund. Math. 160 (1999) 219-246.
[.pdf]
-
Homeomorphic restrictions of unimodal maps,
Contemp. Math. 246 (1999) 47-56;
[.pdf]
-
Planar embeddings of inverse limit spaces of unimodal maps.
Topology and its Applications 96 (1999) 191-208.
[.pdf]
2000
-
Inverse limit spaces of post-critically finite tent maps.
Fund. Math. 165 (2000) 125-138
[.pdf]
-
Dimensions of recurrence times and minimal subshifts,
Conference Proceedings: from Chrystal to Chaos, Luminy
(2000),
[.pdf]
2001
- (with Jane Hawkins)
Exactness and maximal automorphic factors of unimodal
maps,
Ergod. Th. and Dyn. Sys. 21 (2001) 1009-1034;
[.pdf]
- (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]
2002
- (with Dierk Schleicher)
Symbolic dynamics of quadratic polynomials.
Preprint (2002)
This is available on the web-pages of the
Mittag-Leffler institute.
2003
- (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]
-
(with Benoit Saussol, Serge Troubetzkoy and Sandro Vaienti)
Return time statistics via inducing,
Ergod. Th. and Dyn. Sys. 23 (2003) 991-1013;
[.pdf]
- (with Sebastian van Strien)
Expansion of derivatives in one-dimensional dynamics,
Isr. J. Math. 137 (2003) 223-263.
[.pdf]
- (with Sergiy Kolyada and L'ubomir Snoha)
Minimal nonhomogeneous continua,
Colloq. Math. 95 (2003) 123-132.
[.pdf]
- (with Sandro Vaienti)
Return time statistics for unimodal maps.
Fund. Math. 176 (2003) 77--94.
[.pdf]
-
Minimal Cantor systems and unimodal maps.
J. Difference Eq. and Appl. 9 (2003) 305--318.
[.pdf]
- (with Serge Troubetzkoy)
The Gauss map on a class of interval translation mappings.
Isr. J. Math. 137 (2003) 125-148.
[.pdf]
- (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]
- (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]
2004
- (with Martijn van Noort)
Nonconformal perturbations of z -> z 2 + c: the 1:3 resonance,
Nonlinearity 17 (2004) 765 - 789
[.pdf]
2005
-
Asymptotic arc-components of unimodal inverse limit spaces,
Top. & Appl. 152 (2005) 182 - 200.
[.pdf]
- (with Karen Brucks)
Topics from one-dimensional dynamics,
London Mathematical Society, Student Texts 62
Cambridge University Press 2004. Available at
Cambridge University Press
- (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]
- (with Mark Holland and Matt Nicol)
Livsic regularity for Markov systems,
Ergod. Th. and Dyn. Sys. 25 (2005) 1739-1766.
[.pdf]
- (with Oksana Volkova)
The complexity of Fibonacci-like kneading sequences,
Theo. Comp. Science. 377 (2005) 379-389.
[.pdf]
2006
- (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]
- (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]
- (with Mike Todd)
Markov extensions and lifting measures for complex polynomials,
[.pdf]
Ergod. Th. and Dyn. Sys. 27 (2007) 743-768.
-
Renormalisation in a class of interval translation
maps of d branches,
Dynamical Systems, an international journal 22 (2007) 11 - 24.
Preprint version 2006.
[.pdf]
-
Subcontinua of Fibonacci-like unimodal inverse limit spaces.
Topology Proceedings 31 (2007) no. 1, 37-50.
[.pdf]
- (with Mike Todd)
Complex maps without invariant densities,
Nonlinearity 19 (2006) 2929-2945.
Preprint (Version October 2006).
[.pdf]
2007
- (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]
- (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].
- (with Jane Hawkins)
Rigidity of smooth one-sided Bernoulli endomorphisms,
Preprint 2007 - revised 2009,
[.pdf]
New York Journal
of Maths. 15 (2009), 451-483.
-
Combinatorics of (Fibonacci-like) unimodal maps.
Notes used for Spring School at Luminy, April 2006,
"Séminaires et Congrès" 20 17-37 (2010).
[.pdf]
2008
- (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]
- (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]
- (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.
- (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]
- (with Jonathan Deane)
Piecewise contractions are asymptotically periodic,
Proc. Amer. Math. Soc. 137 (2009), 1389-1395.
[.pdf]
- (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]
-
(Non)invertibility of Fibonacci-like unimodal maps
restricted to their critical omega-limit sets.
Preprint 2008.
[.pdf],
Topology Proceedings 37 (2011) 459-480.
- (with Alexandra Kaffl and Dierk Schleicher)
Existence of quadratic Hubbard trees.
Fund. Math. 202 (2009) 251-279,
[.pdf]
- (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)
2009
- (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
- (with Sebastian van Strien)
Monotonicity of entropy for real multimodal maps
Preprint 2009, revised version of December 2013
[.pdf].
J. Amer. Math. Soc. 28 (2015), no. 1, 1-61.
- (with Marcy Barge and Sonja Štimac)
The Ingram conjecture
Updated preprint version July 2011
[.pdf]
Geom. Topol. 16 (2012), 2481-2516.
- (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)
2010
- (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
- (with Sonja Štimac)
On isotopy and unimodal inverse limit spaces
Preprint 2011, [.pdf],
Discrete and Continuous Dynamical Systems
32 (2012), no. 4, 1245-1253.
- (with Renaud Leplaideur)
Renormalization, thermodynamic formalism and quasi-crystals in subshifts.
Preprint 2010 (updated 2012) [.pdf]
Commun. Math. Phys. 321 (2013), 209-247.
DOI: 10.1007/s00220-012-1651-4
2011
- (with Jozef Bobok)
The topological entropy of Banach spaces
Preprint 2011 [.pdf]
J. Difference Equ. Appl. 18 (2012), no. 4, 569-578.
- (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
- (with Greg Clack)
Inducing and unique ergodicity of double rotations
Preprint 2011 [.pdf],
Discrete and Continuous Dynamical Systems
32, no. 12 2012, 4133-4147.
Click here for the electronic version of the journal.
2012
- (with Mike Todd)
Wild attractors and thermodynamic formalism,
Preprint 2012 [.pdf]
Monatshefte für Mathematik,
178 (2015), 39-83.
DOI: 10.1007/s00605-015-0747-2
- (with Dierk Schleicher)
Bernoulli measure of complex admissible kneading sequences,
Preprint 2012 [.pdf]
Ergod. Th. Dyn. Sys. 33 2013, 821-830.
DOI: 10.1017/edts.2012.134
- (with Dierk Schleicher)
Hausdorff dimension of biaccessible angles for quadratic polynomials,
Preprint 2012 and revised 2016 [.pdf]
Fund. Math. 238 (2017), 201-240
DOI: 10.4064/fm276-6-2016
-
On double spirals in Fibonacci-like unimodal inverse limit spaces,
[.pdf] Topology Proc. 43 (2014), 83-97.
and
Erratum Topology Proc. 49 (2017), 251-252.
-
Lebesgue ergodicity of a dissipative subtractive algorithm,
[.pdf]
Springer Proceedings in Mathematics 70 (2014), 105-117.
- (with Sonja Štimac)
Entropy of homeomorphisms on unimodal inverse limit spaces,
[.pdf]
Nonlinearity 26 (2013) 991-1000,
and Corrigendum, Nonlinearity 31 (2018), no. 8, C1-C3.
See also corrigendum
and corrected preprint
version.
2013
- (with Sebastian van Strien)
On the structure of isentropes of polynomial maps,
[.pdf]
Dynamical Systems: an international journal. 28 (2013) 381-392.
- (with Robbert Fokkink and Cor Kraaikamp)
The convergence of the generalised Selmer algorithm,
Preprint 2013 revised 2014 [.pdf]
Israel J. Math. 209 (2015), no. 2, 803-823.
Erratum: Israel Journal of Mathematics, (), 1
DOI 10.1007/s11856-019-1861-y
- (with Sonja Štimac)
Fibonacci-like unimodal inverse limit spaces
and the core Ingram conjecture,
Preprint 2013 and revised 2014 [.pdf].
Topological Methods in Nonlinear Analysis (TMNA)
47 (2016), 147--185. doi: 10.12775/TMNA.2016.001
- (with Charlene Kalle)
Natural extensions for piecewise affine maps via Hofbauer towers,
Preprint 2013 [.pdf]
Monatsh. Math. 175 (2014), no. 1, 65-88.
Springer publication:
(DOI)
10.1007/s00605-014-0644-0
- (with Robbert Fokkink, Guoyong Gu and Cees Roos)
On the chaotic behavior of the primal-dual affine scaling algorithm for linear optimization,
Preprint 2013 [.pdf].
Chaos 24 , 043132 (2014); DOI: 10.1063/1.4902900
- (with Renaud Leplaideur)
Renormalization, freezing phase transitions and Fibonacci
quasicrystals,
Preprint 2013 [.pdf].
Ann. Sc. Ecole Normale Supérieur
48 (2015), no. 3, 739-763.
2014
- (with Piotr Oprocha)
On "observable" Li-Yorke tuples for interval maps,
Preprint 2014. [.pdf]
Nonlinearity 28 (2015) 1675-1694.
(click for the published article)
-
The work of Y. Sinai; on the occasion of him receiving the Abel Prize 2014,
[.pdf] Internationale Mathematische Nachrichten (IMN) 226 (2014), 21-26.
- (with Dalia Terhesiu)
A renewal scheme for non-uniformly hyperbolic semiflows
Preprint 2014 and updated January 2015 (in this last update,
the paper was split into this one, and the one below. [.pdf]
2015
- (with Dalia Terhesiu)
Verifying abstract hypotheses used in obtaining mixing rates
for some non-uniformly hyperbolic semiflows
Preprint 2015 [.pdf].
- (with Dalia Terhesiu)
Upper and lower bounds for the correlation function via inducing with general return times
Preprint 2015 [.pdf].
Ergod. Th. and Dyn. Sys. 38
(2018) 34-62. DOI: http://dx.doi.org/10.1017/etds.2016.20
- (with Ana Anušić and Jernej Činč)
The Core Ingram Conjecture for non-recurrent critical points
Preprint 2015, revision 2016 [.pdf]
Fund. Math. 241 (2018), no. 3, 209-235.
2016
- (with Jozef Bobok)
Constant slope maps and the Vere-Jones classification.
Preprint 2016 [.pdf].
Entropy 18(6) , 234, 2016. doi:10.3390/e18060234
- (with Ana Anušić and Jernej Činč)
Uncountably many planar embeddings of unimodal inverse limit spaces
Preprint 2016 [.pdf].
Discrete Contin. Dyn. Syst. 37 (2017), no. 5, 2285-2300.
- (with Dalia Terhesiu)
The Dolgopyat inequality in BV for non-Markov maps
[.pdf]
Stochastics and Dynamics, 18 (2018), no. 2, 1850006, 44 pp.
doi.org/10.1142/S0219493718500065
- (with Ian Melbourne and Dalia Terhesiu)
Rates of mixing for nonMarkov infinite measure semiflows
Preprint 2016 [.pdf].
Trans. AMS. 371 (2019), no. 10, 7343-7386.
- (with Mark Demers and Mike Todd)
Hitting and escaping statistics: mixing, targets and holes,
Preprint 2016 (updated December 2017) [.pdf]
Adv. Math. 328 (2018), 1263-1298.
- (with Carlo Carminati and Charlene Kalle)
Matching for generalised β-transformations,
Preprint 2016 [.pdf],
arXiv version.
Indagationes Mathematicae,
28 (2017), no. 1, 55-73.
DOI: 10.1016/j.indag.2016.11.005.
2017
- (with Sonja Štimac)
On isotopy of self-homeomorphisms of quadratic inverse limit spaces
Preprint July 217 [.pdf].
arXiv version,
Topology Proceedings 52 (2018), 167-177
- (with Carlo Carminati, Stefano Marmi and Alessandro Profeti)
Matching in a family of piecewise affine interval maps,
Preprint July 2016 [.pdf],
arXiv version.
Nonlinearity 32 (2018), 172-208.
- (with Dalia Terhesiu)
Regular variation and rates of mixing for infinite measure preserving
almost Anosov diffeomorphisms
Preprint 2017 (updated Jan 2018) [.pdf]
arXiv version.
Ergod. Th. and Dyn. Sys. 40 2020, 663-698, doi.org/10.1017/etds.2018.58).
- (with Dalia Terhesiu and Mike Todd)
The pressure function for infinite equilibrium measures
Preprint 2017 [.pdf]
arXiv version.
Israel J. Math. 232 (2019), 775-826.
Doi: s11856-019-1887-1
2018
- (with Ana Anušić and Jernej Činč)
Problems on planar embeddings of
chainable continua and accessibility.
In:
Problems in Continuum Theory in Memory of Sam B. Nadler, Jr.
Ed. Logan Hoehn, Piotr Minc, Murat Tuncali,
Topology Proceedings 52 2018, 283-285 in
[pdf]
and the Auburn source.
- (with Ana Anušić and Jernej Činč)
Planar embeddings of chainable continua.
Preprint 2018 [.pdf],
to appear in Topology Proceedings.
- (with Ian Melbourne and Dalia Terhesiu)
Sharp polynomial bounds on decay of correlations for multidimensional
nonuniformly hyperbolic systems and billiards.
Preprint 2018 [.pdf] and
arXiv version (updated November 15 2019).
To appear in Ann. Henri Lebesgue.
- (with Dalia Terhesiu and Mike Todd)
Pressure function and limit theorems for almost Anosov flows.
Preprint 2018 [.pdf] and
arXiv version.
-
An overview of unimodal inverse limit spaces inverse limit spaces.
[.pdf]
Conference proceeding and minicourse notes for the conference
``Interval dynamics and Inverse limit spaces'',
at IWCTA: International Workshop and Conference on Topology & Applications,
Rajagiri School of Engineering & Technology, Kochi, December 5-8 2018.
2019
- (with Lori Alvin, Ana Anušić and Jernej Činč)
Folding points of unimodal inverse limit spaces.
Preprint 2019 [.pdf],
Nonlinearity 33 (2020), 224-248.
Doi: 10.1088/1361-6544/ab4e31
-
On volume preserving almost Anosov flows.
Preprint 2019 updated 2020 [.pdf]
and arXiv version
- (with Ana Anušić and Jernej Činč)
Topological properties of Lorenz maps derived from unimodal maps
Preprint 2019 [.pdf],
Journal of Difference Equations and Dynamics, 26 Issue 8, 1174-1191.
2020
-
On Sinai billiards on flat surfaces with horns.
Preprint 2020 (revisewd Jan. 2021) [.pdf]
and arXiv version
- (with Benjamin Vejnar)
Classification of one dimensional dynamical systems by countable structures.
Preprint 2020 [.pdf],
and arXiv version
2021
- (with Olga Lukina)
Rotated odometers.
Preprint 2021 [.pdf],
and arXiv version
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