Research outputs
Selected research outputs
- Dynamic rays of bounded-type entire functions (Journal article - 2007)
- Rigidity of escaping dynamics for transcendental entire functions (Journal article - 2006)
- Bifurcations in the space of exponential maps (Journal article - 2003)
- Density of hyperbolicity for classes of real transcendental entire functions and circle maps (Journal article - 2015)
- Singular orbits and Baker domains (Journal article - 2020)
- A landing theorem for entire functions with bounded post-singular sets (Journal article - 2017)
- On Connected Preimages of Simply-Connected Domains Under Entire Functions (Journal article - 2019)
- Hyperbolic entire functions with bounded Fatou components (Journal article - 2014)
- Absence of wandering domains for some real entire functions with bounded singular sets (Journal article - 2011)
- Siegel disks and periodic rays of entire functions (Journal article - 2004)
2025
Eremenko's conjecture, wandering Lakes of Wada, and maverick points
Marti-Pete, D., Rempe, L., & Waterman, J. (2025). Eremenko's conjecture, wandering Lakes of Wada, and maverick points. Journal of The American Mathematical Society.
Spiders’ Webs in the Eremenko–Lyubich Class
Rempe, L. (2025). Spiders’ Webs in the Eremenko–Lyubich Class. International Mathematics Research Notices, 2025(3). doi:10.1093/imrn/rnae278
Bounded Fatou and Julia components of meromorphic functions
Martí-Pete, D., Rempe, L., & Waterman, J. (2024). Bounded Fatou and Julia components of meromorphic functions. Mathematische Annalen. doi:10.1007/s00208-023-02725-4
Points of Convergence—Music Meets Mathematics
Rempe, L. (2025). Points of Convergence—Music Meets Mathematics. In Mathematics in Industry (pp. 265-271). Springer Nature Switzerland. doi:10.1007/978-3-031-48683-8_33
2024
Second order linear differential equations with a basis of solutions having only real zeros
Bergweiler, W., Eremenko, A., & Rempe, L. (2024). Second order linear differential equations with a basis of solutions having only real zeros. Journal d'Analyse Mathématique, 152(1), 53-108. doi:10.1007/s11854-023-0294-z
2023
The Eremenko–Lyubich constant
Rempe, L. (2022). The Eremenko–Lyubich constant. Bulletin of the London Mathematical Society. doi:10.1112/blms.12714
2022
Geometrically finite transcendental entire functions
Alhamed, M., Rempe, L., & Sixsmith, D. (2022). Geometrically finite transcendental entire functions. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 106(2), 485-527. doi:10.1112/jlms.12516
2021
Geometrically finite transcendental entire functions
Alhamed, M., Rempe, L., & Sixsmith, D. (n.d.). Geometrically finite transcendental entire functions. Retrieved from http://arxiv.org/abs/2003.08884v3
2020
Singular orbits and Baker domains
Rempe, L. (n.d.). Singular orbits and Baker domains. Retrieved from http://arxiv.org/abs/2009.07020v1
A landing theorem for entire functions with bounded post-singular sets
Benini, A. M., & Rempe, L. (n.d.). A landing theorem for entire functions with bounded post-singular sets. Retrieved from http://arxiv.org/abs/1711.10780v4
Singular orbits and Baker domains
Rempe, L. (2022). Singular orbits and Baker domains. MATHEMATISCHE ANNALEN, 382(3-4), 1475-1483. doi:10.1007/s00208-020-02132-z
Escaping sets are not sigma-compact
Rempe, L. (2022). ESCAPING SETS ARE NOT SIGMA-COMPACT. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 150(1), 171-177. doi:10.1090/proc/15576
A landing theorem for entire functions with bounded post-singular sets
Benini, A. M., & Rempe-Gillen, L. (n.d.). A landing theorem for entire functions with bounded post-singular sets. Retrieved from http://arxiv.org/abs/1711.10780v3
Geometrically finite transcendental entire functions
Alhamed, M., Rempe, L., & Sixsmith, D. (2020). Geometrically finite transcendental entire functions. J. London Math. Soc., 106 (2022), 485-527. Retrieved from http://dx.doi.org/10.1112/jlms.12516
Fatou’s Associates
Evdoridou, V., Rempe, L., & Sixsmith, D. J. (2020). Fatou's associates. Arnold Mathematical Journal 6 (2020), 459-493. Retrieved from http://dx.doi.org/10.1007/s40598-020-00148-6
2019
On Connected Preimages of Simply-Connected Domains Under Entire Functions
Rempe-Gillen, L., & Sixsmith, D. (2019). On Connected Preimages of Simply-Connected Domains Under Entire Functions. Geometric and Functional Analysis, 29(5), 1579-1615. doi:10.1007/s00039-019-00488-2
2017
A landing theorem for entire functions with bounded post-singular sets
Benini, A. M., & Rempe-Gillen, L. (2020). A landing theorem for entire functions with bounded post-singular sets. Geometric and Functional Analysis, 30(6), 1465-1530. doi:10.1007/s00039-020-00551-3
Non-escaping endpoints do not explode
Evdoridou, V., & Rempe-Gillen, L. (2018). Non-escaping endpoints do not explode. Bulletin of the London Mathematical Society, 50(5), 916-932. doi:10.1112/blms.12176
2015
Escaping Endpoints Explode
Alhabib, N., & Rempe-Gillen, L. (2017). Escaping Endpoints Explode. COMPUTATIONAL METHODS AND FUNCTION THEORY, 17(1), 65-100. doi:10.1007/s40315-016-0169-8
Non-autonomous conformal iterated function systems and moran-set constructions
Rempe-Gillen, L., & Urbański, M. (2015). Non-autonomous conformal iterated function systems and Moran-set constructions. Transactions of the American Mathematical Society, 368, 1979-2017. doi:10.1090/tran/6490
Density of hyperbolicity for classes of real transcendental entire functions and circle maps
Rempe-Gillen, L., & van Strien, S. (2015). Density of hyperbolicity for classes of real transcendental entire functions and circle maps. Duke Mathematical Journal, 164(6), 1079-1137. doi:10.1215/00127094-2885764
Hyperbolic entire functions and the Eremenko–Lyubich class: Class B or not class B ?
Rempe-Gillen, L., & Sixsmith, D. (2017). Hyperbolic entire functions and the Eremenko-Lyubich class: Class B or not class B?. Mathematische Zeitschrift, 286, 783-800. doi:10.1007/s00209-016-1784-9
2014
The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics
Shen, Z., & Rempe-Gillen, L. (2015). The Exponential Map Is Chaotic: An Invitation to Transcendental Dynamics. AMERICAN MATHEMATICAL MONTHLY, 122(10), 919-940. doi:10.4169/amer.math.monthly.122.10.919
Hyperbolic entire functions with full hyperbolic dimension and approximation by Eremenko-Lyubich functions
Rempe, L. (2014). Hyperbolic entire functions with full hyperbolic dimension and approximation by Eremenko-Lyubich functions. Proceedings of the London Mathematical Society, 108(5), 1193-1225. doi:10.1112/plms/pdt048
Hyperbolic entire functions with bounded Fatou components
Bergweiler, W., Fagella, N., & Rempe-Gillen, L. (2015). Hyperbolic entire functions with bounded Fatou components. Commentarii Mathematici Helvetici, 90(4), 799-823. doi:10.4171/CMH/371
2013
Primality Testing for Beginners
Rempe-Gillen, L., & Waldecker, R. (2013). Primality Testing for Beginners. American Mathematical Society. doi:10.1090/stml/070
On invariance of order and the area property for finite-type entire functions
Epstein, A., & Rempe-Gillen, L. (2015). ON INVARIANCE OF ORDER AND THE AREA PROPERTY FOR FINITE-TYPE ENTIRE FUNCTIONS. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 40(2), 573-599. doi:10.5186/aasfm.2015.4034
2011
Absence of wandering domains for some real entire functions with bounded singular sets
Mihaljevic-Brandt, H., & Rempe-Gillen, L. (2013). Absence of wandering domains for some real entire functions with bounded singular sets. MATHEMATISCHE ANNALEN, 357(4), 1577-1604. doi:10.1007/s00208-013-0936-z
Brushing the hairs of transcendental entire functions
Baranski, K., Jarque, X., & Rempe, L. (2012). Brushing the hairs of transcendental entire functions. TOPOLOGY AND ITS APPLICATIONS, 159(8), 2102-2114. doi:10.1016/j.topol.2012.02.004
2010
Rigidity and absence of line fields for meromorphic and Ahlfors islands maps
Mayer, V., & Rempe, L. (2012). Rigidity and absence of line fields for meromorphic and Ahlfors islands maps. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 32, 1691-1710. doi:10.1017/S0143385711000332
Exotic baker and wandering domains for Ahlfors islands maps
Rempe, L., & Rippon, P. J. (2012). Exotic baker and wandering domains for Ahlfors islands maps. JOURNAL D ANALYSE MATHEMATIQUE, 117, 297-319. doi:10.1007/s11854-012-0023-5
2009
Connected escaping sets of exponential maps
Rempe, L. (2011). CONNECTED ESCAPING SETS OF EXPONENTIAL MAPS. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 36(1), 71-80. doi:10.5186/aasfm.2011.3604
Hausdorff dimensions of escaping sets of transcendental entire functions
Rempe, L., & Stallard, G. M. (2010). HAUSDORFF DIMENSIONS OF ESCAPING SETS OF TRANSCENDENTAL ENTIRE FUNCTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 138(5), 1657-1665. Retrieved from https://www.webofscience.com/
Are Devaney hairs fast escaping?
Rempe, L., Rippon, P. J., & Stallard, G. M. (2009). Are Devaney hairs fast escaping?. J. Difference Equ. Appl., 16 (2010), no. 5-6, 739-762. Retrieved from http://dx.doi.org/10.1080/10236190903282824
Primzahltests für Einsteiger
Rempe, L., & Waldecker, R. (2009). Primzahltests für Einsteiger. Vieweg+Teubner. doi:10.1007/978-3-8348-9597-4
2008
The escaping set of the exponential
Rempe, L. (2010). The escaping set of the exponential. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 30, 595-599. doi:10.1017/S014338570900008X
A note on hyperbolic leaves and wild laminations of rational functions
Kahn, J., Lyubich, M., & Rempe, L. (2010). A note on hyperbolic leaves and wild laminations of rational functions. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 16(5-6), 655-665. doi:10.1080/10236190903257867
Bifurcation Loci of Exponential Maps and Quadratic Polynomials: Local Connectivity, Triviality of Fibers, and Density of Hyperbolicity
Rempe, L., & Schleicher, D. (2008). Bifurcation Loci of Exponential Maps and Quadratic Polynomials: Local Connectivity, Triviality of Fibers, and Density of Hyperbolicity. In Unknown Book (Vol. 53, pp. 177-+). Retrieved from https://www.webofscience.com/
Absence of line fields and Mañé's theorem for nonrecurrent transcendental functions
Rempe, L., & van Strien, S. (2011). ABSENCE OF LINE FIELDS AND MANE'S THEOREM FOR NONRECURRENT TRANSCENDENTAL FUNCTIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(1), 203-228. doi:10.1090/S0002-9947-2010-05125-6
2007
HYPERBOLIC DIMENSION AND RADIAL JULIA SETS OF TRANSCENDENTAL FUNCTIONS
Rempe, L. (2009). HYPERBOLIC DIMENSION AND RADIAL JULIA SETS OF TRANSCENDENTAL FUNCTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 137(4), 1411-1420. Retrieved from https://www.webofscience.com/
Dynamic rays of bounded-type entire functions
Rottenfusser, G., Rueckert, J., Rempe, L., & Schleicher, D. (2011). Dynamic rays of bounded-type entire functions. ANNALS OF MATHEMATICS, 173(1), 77-125. doi:10.4007/annals.2011.173.1.3
2006
On a question of Eremenko concerning escaping components of entire functions
Rempe, L. (2007). On a question of Eremenko concerning escaping components of entire functions. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 39, 661-666. doi:10.1112/blms/bdm053
Rigidity of escaping dynamics for transcendental entire functions
Rempe, L. (2009). Rigidity of escaping dynamics for transcendental entire functions. ACTA MATHEMATICA, 203(2), 235-267. doi:10.1007/s11511-009-0042-y
2005
On nonlanding dynamic rays of exponential maps
Rempe, L. (2007). On nonlanding dynamic rays of exponential maps. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 32(2), 353-369. Retrieved from https://www.webofscience.com/
2004
Siegel disks and periodic rays of entire functions
Rempe, L. (2008). Siegel disks and periodic rays of entire functions. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 624, 81-102. doi:10.1515/CRELLE.2008.081
Combinatorics of Bifurcations in Exponential Parameter Space
Rempe, L., & Schleicher, D. (2004). Combinatorics of Bifurcations in Exponential Parameter Space. London Mathematical Society Lecture Note Series, 348, 317-370. Retrieved from http://arxiv.org/abs/math/0408011v2
2003
Bifurcations in the space of exponential maps
Rempe, L., & Schleicher, D. (2009). Bifurcations in the space of exponential maps. INVENTIONES MATHEMATICAE, 175(1), 103-135. doi:10.1007/s00222-008-0147-5
Classification of escaping exponential maps
Foerster, M., Rempe, L., & Schleicher, D. (2008). Classification of escaping exponential maps. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136(2), 651-663. Retrieved from https://www.webofscience.com/
Topological dynamics of exponential maps on their escaping sets
Rempe, L. (2006). Topological dynamics of exponential maps on their escaping sets. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 26, 1939-1975. doi:10.1017/S0143385706000435
On prime ends and local connectivity
Rempe, L. (2008). On prime ends and local connectivity. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 40, 817-826. doi:10.1112/blms/bdn061
A landing theorem for periodic rays of exponential maps
Rempe, L. (2006). A landing theorem for periodic rays of exponential maps. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134(9), 2639-2648. doi:10.1090/S0002-9939-06-08287-6
On a question of Herman, Baker and Rippon concerning Siegel disks
Rempe, L. (2004). On a question of Herman, Baker and Rippon concerning Siegel disks. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 36, 516-518. doi:10.1112/S0024609304003157