Papers and Preprints

(as of September 2024)


List of Publications

I no longer actively maintain a list of publications on this page; instead my list of recent publications and preprints from arxiv.org is shown below automatically, courtesy of the myarticles widget. You can also use the following resources:
  • My ORCID record. (The open and non-profit ORCID system provides a unique researcher ID that can be associated to articles and is highly recommended.)
  • Preprint versions of all my papers on arxiv.org.
  • You can find a list of my publications, and associated reviews, on MathSciNet if you are connecting from a subscribing institution.
  • My (only occasionally maintained) Google Scholar Profile.

    See below in addition for Theses and Books that do not appear on the above lists, as well as a (sporadically maintained) list of errata.


    Lasse Rempe's articles on arXiv

    [1]  http://arxiv.org/abs/2209.03284v3 [ html pdf ]
    Entire functions with Cantor bouquet Julia sets
    Leticia Pardo-Simón, Lasse Rempe
    [2]  http://arxiv.org/abs/2410.20998v3 [ html pdf ]
    Spiders' webs in the Eremenko-Lyubich class
    Lasse Rempe
    Journal ref: International Mathematics Research Notices, Volume 2025, Issue 3, February 2025
    [3]  http://arxiv.org/abs/2108.10256v5 [ html pdf ]
    Eremenko's conjecture, wandering Lakes of Wada, and maverick points
    David Martí-Pete, Lasse Rempe, James Waterman
    [4]  http://arxiv.org/abs/2405.12165v1 [ html pdf ]
    Classifying multiply connected wandering domains
    Gustavo Rodrigues Ferreira, Lasse Rempe
    [5]  http://arxiv.org/abs/2309.06595v1 [ html pdf ]
    Points of convergence -- music meets mathematics
    Lasse Rempe
    [6]  http://arxiv.org/abs/2204.11781v2 [ html pdf ]
    Bounded Fatou and Julia components of meromorphic functions
    David Martí-Pete, Lasse Rempe, James Waterman
    [7]  http://arxiv.org/abs/1711.10780v5 [ html pdf ]
    A landing theorem for entire functions with bounded post-singular sets
    Anna Miriam Benini, Lasse Rempe
    Journal ref: Geometric and Functional Analysis 30 (2020), 1465--1530
    [8]  http://arxiv.org/abs/2105.09053v2 [ html pdf ]
    The Eremenko-Lyubich constant
    Lasse Rempe
    Journal ref: Bull. London Math. Soc., 55 (2023), 113-118
    [9]  http://arxiv.org/abs/2204.08949v2 [ html pdf ]
    Second order linear differential equations with a basis of solutions having only real zeros
    Walter Bergweiler, Alexandre Eremenko, Lasse Rempe
    Journal ref: J. Anal. Math. 152 (2024), no. 1, 53-108
    [10]  http://arxiv.org/abs/2103.16702v2 [ html pdf ]
    Non-compact Riemann surfaces are equilaterally triangulable
    Christopher J. Bishop, Lasse Rempe
    [11]  http://arxiv.org/abs/2105.10391v1 [ html pdf ]
    A bouquet of pseudo-arcs
    Tania Gricel Benitez, Lasse Rempe
    [12]  http://arxiv.org/abs/2006.16946v4 [ html pdf ]
    Escaping sets are not sigma-compact
    Lasse Rempe
    Journal ref: Proc. Amer. Math. Soc. 150 (2022), No. 1, 171--177
    [13]  http://arxiv.org/abs/2003.08884v3 [ html pdf ]
    Geometrically finite transcendental entire functions
    Mashael Alhamed, Lasse Rempe, Dave Sixsmith
    Journal ref: J. London Math. Soc., 106 (2022), 485-527
    [14]  http://arxiv.org/abs/2009.07020v2 [ html pdf ]
    Singular orbits and Baker domains
    Lasse Rempe
    Journal ref: Math. Ann. 382 (2022), 1475-1483
    [15]  http://arxiv.org/abs/2002.03320v4 [ html pdf ]
    Fatou's associates
    Vasiliki Evdoridou, Lasse Rempe, David J. Sixsmith
    Journal ref: Arnold Mathematical Journal 6 (2020), 459-493
    [16]  http://arxiv.org/abs/2001.06353v1 [ html pdf ]
    Eventual hyperbolic dimension of entire functions and Poincar\'e functions of polynomials
    Alexandre DeZotti, Lasse Rempe-Gillen
    [17]  http://arxiv.org/abs/1610.06278v4 [ html pdf ]
    Arc-like continua, Julia sets of entire functions, and Eremenko's Conjecture
    Lasse Rempe-Gillen
    [18]  http://arxiv.org/abs/1801.06359v3 [ html pdf ]
    On connected preimages of simply-connected domains under entire functions
    Lasse Rempe-Gillen, Dave Sixsmith
    Journal ref: Geom. Funct. Anal. 29 (2019), 1579-1615
    [19]  http://arxiv.org/abs/1707.01843v2 [ html pdf ]
    Non-escaping endpoints do not explode
    Vasiliki Evdoridou, Lasse Rempe-Gillen
    Journal ref: Bull. London Math. Soc. 50 (2018) 916-932
    [20]  http://arxiv.org/abs/1502.00492v2 [ html pdf ]
    Hyperbolic entire functions and the Eremenko-Lyubich class: Class $\mathcal{B}$ or not class $\mathcal{B}$?
    Lasse Rempe-Gillen, Dave Sixsmith
    Journal ref: Math. Z. 286 (2017), 783-800
    [21]  http://arxiv.org/abs/1506.05347v2 [ html pdf ]
    Escaping endpoints explode
    Nada Alhabib, Lasse Rempe-Gillen
    Journal ref: Comput. Methods Funct. Theory 17 (2017), 65-100
    [22]  http://arxiv.org/abs/1404.0925v2 [ html pdf ]
    Hyperbolic entire functions with bounded Fatou components
    Walter Bergweiler, Núria Fagella, Lasse Rempe-Gillen
    Journal ref: Comment. Math. Helv. 90 (2015), 799-829
    [23]  http://arxiv.org/abs/1408.1129v2 [ html pdf ]
    The exponential map is chaotic: An invitation to transcendental dynamics
    Zhaiming Shen, Lasse Rempe-Gillen
    Journal ref: Amer. Math. Monthly 122 (2015), 919-940
    [24]  http://arxiv.org/abs/1304.6576v3 [ html pdf ]
    On invariance of order and the area property for finite-type entire functions
    Adam Epstein, Lasse Rempe-Gillen
    Journal ref: Ann. Acad. Sci. Fenn. Math. 40 (2015), no. 2, 573-599
    [25]  http://arxiv.org/abs/1005.4627v5 [ html pdf ]
    Density of hyperbolicity for classes of real transcendental entire functions and circle maps
    Lasse Rempe-Gillen, Sebastian van Strien
    Journal ref: Duke Math. J. 164, no. 6 (2015), 1079-1137
    [26]  http://arxiv.org/abs/1210.7469v4 [ html pdf ]
    Non-autonomous conformal iterated function systems and Moran-set constructions
    Lasse Rempe-Gillen, Mariusz Urbański
    Journal ref: Trans. Amer. Math. Soc. 368 (2016), 1979-2017
    [27]  http://arxiv.org/abs/math/0309022v6 [ html pdf ]
    Prime Ends and Local Connectivity
    Lasse Rempe-Gillen
    Journal ref: Bull. London Math. Soc. 40 (2008), No. 5, 817-826
    [28]  http://arxiv.org/abs/1104.0034v2 [ html pdf ]
    Absence of wandering domains for some real entire functions with bounded singular sets
    Helena Mihaljević-Brandt, Lasse Rempe-Gillen
    Journal ref: Math. Ann. 357 (2013), no. 4, 1577-1604
    [29]  http://arxiv.org/abs/1106.3439v3 [ html pdf ]
    Hyperbolic entire functions with full hyperbolic dimension and approximation by Eremenko-Lyubich functions
    Lasse Rempe-Gillen
    Journal ref: Proc. London Math. Soc. (2014) 108 (5), 1193-1225
    [30]  http://arxiv.org/abs/1101.4209v2 [ html pdf ]
    Brushing the hairs of transcendental entire functions
    Krzysztof Barański, Xavier Jarque, Lasse Rempe
    Journal ref: Topology Appl. 159 (2012), no. 8, 2102-2114
    [31]  http://arxiv.org/abs/1012.4951v1 [ html pdf ]
    Rigidity and absence of line fields for meromorphic and Ahlfors islands maps
    Volker Mayer, Lasse Rempe
    Journal ref: Ergodic Theory Dynam. Systems 32 (2012), No. 5, 1691-1710
    [32]  http://arxiv.org/abs/1008.1724v1 [ html pdf ]
    Exotic Baker and wandering domains for Ahlfors islands maps
    Lasse Rempe, Philip J. Rippon
    Journal ref: J. Anal. Math. 117 (2012), 297-319
    [33]  http://arxiv.org/abs/0802.0666v3 [ html pdf ]
    Absence of line fields and Mane's theorem for non-recurrent transcendental functions
    Lasse Rempe, Sebastian van Strien
    Journal ref: Trans. Amer. Math. Soc. 363 (2011), 203-228
    [34]  http://arxiv.org/abs/0910.4680v2 [ html pdf ]
    Connected escaping sets of exponential maps
    Lasse Rempe
    Journal ref: Ann. Acad. Sci. Fenn. 36 (2011), 71-80
    [35]  http://arxiv.org/abs/0904.3072v1 [ html pdf ]
    Hausdorff dimensions of escaping sets of transcendental entire functions
    Lasse Rempe, Gwyneth M. Stallard
    Journal ref: Proc. Amer. Math. Soc. 138 (2010), 1657-1665.
    [36]  http://arxiv.org/abs/0904.1403v1 [ html pdf ]
    Are Devaney hairs fast escaping?
    Lasse Rempe, Philip J. Rippon, Gwyneth M. Stallard
    Journal ref: J. Difference Equ. Appl., 16 (2010), no. 5-6, 739-762
    [37]  http://arxiv.org/abs/0704.3213v2 [ html pdf ]
    Dynamic rays of bounded-type entire functions
    Günter Rottenfußer, Johannes Rückert, Lasse Rempe, Dierk Schleicher
    Journal ref: Ann. of Math. 173 (2011), no. 1, 77-125
    [38]  http://arxiv.org/abs/math/0605058v3 [ html pdf ]
    Rigidity of escaping dynamics for transcendental entire functions
    Lasse Rempe
    Journal ref: Acta Mathematica 203 (2009), no 2, 235 --267
    [39]  http://arxiv.org/abs/0812.1768v1 [ html pdf ]
    The escaping set of the exponential
    Lasse Rempe
    Journal ref: Ergodic Theory and Dynamical Systems (2010), 30:595-599
    [40]  http://arxiv.org/abs/0810.5571v1 [ html pdf ]
    A note on hyperbolic leaves and wild laminations of rational functions
    Jeremy Kahn, Mikhail Lyubich, Lasse Rempe
    Journal ref: J. Difference Equ. Appl., 16 (2010), no. 5-6, 655--665
    [41]  http://arxiv.org/abs/math/0408041v5 [ html pdf ]
    Siegel Disks and Periodic Rays of Entire Functions
    Lasse Rempe
    Journal ref: J. Reine Angew. Math. 624, 81-102 (2008).
    [42]  http://arxiv.org/abs/0805.1658v1 [ html pdf ]
    Bifurcation Loci of Exponential Maps and Quadratic Polynomials: Local Connectivity, Triviality of Fibers, and Density of Hyperbolicity
    Lasse Rempe, Dierk Schleicher
    Journal ref: in: Fields Institute Communications Volume 53: Holomorphic dynamics and renormalization. A volume in honour of John Milnor's 75th birthday (Lyubich et al, eds), 177-196 (2008).
    [43]  http://arxiv.org/abs/0712.4267v1 [ html pdf ]
    Hyperbolic dimension and radial Julia sets of transcendental functions
    Lasse Rempe
    Journal ref: Proc. Amer. Math. Soc. 137 (2009), 1411-1420.
    [44]  http://arxiv.org/abs/math/0311480v6 [ html pdf ]
    Bifurcations in the Space of Exponential Maps
    Lasse Rempe, Dierk Schleicher
    Journal ref: Invent. Math. 175 (2009), No. 1, 103 - 135
    [45]  http://arxiv.org/abs/math/0610453v2 [ html pdf ]
    On a question of Eremenko concerning escaping components of entire functions
    Lasse Rempe
    Journal ref: Bull. London Math. Soc. 39 (2007), no. 4, 661 - 666
    [46]  http://arxiv.org/abs/math/0511588v2 [ html pdf ]
    On Nonlanding Dynamic Rays of Exponential Maps
    Lasse Rempe
    Journal ref: Ann. Acad. Sci. Fenn. Math. 32 (2007), no. 2, 353--369
    [47]  http://arxiv.org/abs/math/0408011v2 [ html pdf ]
    Combinatorics of Bifurcations in Exponential Parameter Space
    Lasse Rempe, Dierk Schleicher
    Journal ref: In: Transcendental dynamics and complex analysis. In honour of Noel Baker (Rippon and Stallard, eds); London Mathematical Society Lecture Note Series 348, 317-370 (2008).
    [48]  http://arxiv.org/abs/math/0311427v6 [ html pdf ]
    Classification of Escaping Exponential Maps
    Markus Förster, Lasse Rempe, Dierk Schleicher
    Journal ref: Proc. Amer. Math. Soc. 136 (2008), 651-663
    [49]  http://arxiv.org/abs/math/0309107v3 [ html pdf ]
    Topological Dynamics of Exponential Maps on their Escaping Sets
    Lasse Rempe
    Journal ref: Ergodic Theory and Dynam. Systems 26 (2006), No. 6, 1939-1975
    [50]  http://arxiv.org/abs/math/0307371v4 [ html pdf ]
    A Landing Theorem for Periodic Rays of Exponential Maps
    Lasse Rempe
    Journal ref: Proc. Amer. Math. Soc. 134 (2006), 2639-2648.

    [ Showing 50 of 51 total entries, additional 1 entries available at arXiv.org ]
    [ This list is powered by an arXiv author id and the myarticles widget ]

    Theses


    Books


    Summaries and errata

    Please see below some misprints and errata. These are very old; I was maintaining a list of misprints and errata on a wiki site, but unfortunately this has been deleted so they are lost! If you have further misprints, please let me know.


    Topological dynamics of exponential maps on their escaping sets

    Ergodic Theory Dynam. Systems 26 (2006), no. 6, 1939 - 1975. arXiv:math.DS/0309107; published version.

    Errata:


    Prime ends and local connectivity

    Bull. London Math. Soc. 40 (2008), no. 4, 817 - 826. arxiv:math.GN/0309022. Published version: Abstract, PDF.

    Note (March 2012):Donald Sarason has kindly pointed out that Theorem 1.1 was proved by Marie Torhorst in 1918 in her dissertation (Über die Randmenge einfach-zusammenhängender ebener Gebiete); the result was published in Math. Z. in 1921. It appears that this result had largely been forgotten: I could not find a single reference to Torhorst on MathSciNet, and no-one I spoke to about my paper while I was preparing it was aware of it either!

    Moreover, Don himself wrote a paper with the exact same title as mine in the 1960s, which reproves Torhorst's result from the work of Ursell and Young, which is the same argument by which Theorem 1.1 is established in my paper. However, his paper was not accepted for publication at the time, as he explains:

    I submitted the paper to the Michigan Math. J., then edited by George Piranian, the person who taught me about prime ends and much more about complex analysis. (George is one of my mathematical heroes.) George discussed the paper with Collingwood, one of his collaborators. Their conclusion was that interest in prime ends at the time was at such a low ebb that the paper was likely to be largely ignored.

    I did publish an abstract of the paper in the Notices of the A.M.S. (Vol 16 (1969), p. 701). At the time the Notices published abstracts of talks given at society meetings, plus what I think were called by-title abstracts, which any member of the society could use to announce a result. If my memory is correct, I received as a result of the abstract only one request for a copy of the paper.

    Don's 1960s manuscript, along with George Piranian's letter and the announcement in the Notices, are contained in this PDF file, which he has kindly allowed me to make available.

    To my knowledge, Theorem 1.3, which a characterization of local connectivity at a point and from which Theorem 1.1 follows using the Ursell-Young result, has not previously appeared elsewhere. (Note, however, that the argument that proves the "only if" direction is the same as the one that appears already in Don's paper, which also contains the "if" direction in the special case that every prime end whose impression contains the point in question is of the first kind.)

    Please read the arXiv version of the paper, which has been updated with a summary of this, as well as additional historical remarks on Marie Torhorst, and why the famous theorem about continuous extension of Riemann maps should be called the Caratheodory-Torhorst theorem.


    Hyperbolic dimension and radial Julia sets of transcendental functions

    Proc. Amer. Math. Soc. 137 (2009), 1411-1420. arXiv:0712.4267; published version.

    Errata:


    Dynamic rays of bounded-type entire functions

    With Günter Rottenfußer, Johannes Rückert and Dierk Schleicher.

    Ann. of Math. 173 (2011), no. 1, 77-125. arxiv:0704.3213; published version.

    Errata: