Publications
Selected publications
- 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)
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
Bounded Fatou and Julia components of meromorphic functions
Martí-Pete, D., Rempe, L., & Waterman, J. (n.d.). Bounded Fatou and Julia components of meromorphic functions. Mathematische Annalen. doi:10.1007/s00208-023-02725-4
2023
The Eremenko–Lyubich constant
Rempe, L. (n.d.). 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. 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. (n.d.). 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