The versions on this page are generally early versions which come with the usual health warning with regards to typos and errors. See the relevant journal for the final version.
Preprints
Papers
55. Variance of the distance to the boundary of convex domains in R^2 and R^3, with A. G. Fletcher, to appear in J. Optim. Theory Appl.
54. Genus g Cantor sets and germane Julia sets, with D. Stoertz and V. Vellis, to appear in Proc. Roy. Soc. Edinburgh Sect. A
53. Geometric function theory on uniformly quasiconformally homogeneous domains, with A. Hahn, J. Math. Anal. Appl., 554, no.1 (2026), 129960.
52. Interpolating quasiregular power mappings, with J. Burkart and D. A. Nicks, Trans. Amer. Math. Soc., 379 (2026), 1351-1370.
51. An analogue of Green's functions for quasiregular maps, with M. Broderius, Conf. Geom. Dyn., 29 (2025), 117-142.
50. Phragmen-Lindelof principles and Julia limiting directions of quasiregular mappings, with J. Steranka, Erg. Th. Dyn. Sys., 45, no.11 (2025), 3325-3343.
49. Triangles and variance of the distance to the boundary, with K. Fletcher and J. Wasiqi, Mathematics Exchange, 18, no.1 (2024), 65-76.
48. Normal families and quasiregular mappings, with D. A. Nicks, Proc. Edin. Math. Soc., 67, no.1 (2024), 79-112.
47. Decomposing multitwists, with V. Vellis, J. Anal. Math., 152, (2024), 421–469.
46. On the mean radius of quasiconformal mappings, with J. Pratscher, Israel J. Math. 261 (2024), 419–443.
45. insideOutside: an accessible algorithm for classifying interior and exterior points, with applications in embryology, with S. E. Strawbridge, A. Kurowski, E. Corujo-Simon, J. Nichols and A. G. Fletcher, Biology Open, (2023) 12 (9): bio060055.
44. Genus 2 Cantor sets, with D. Stoertz, Pacific J. Math., 321, no.2 (2022), 283-307.
43. The maximum modulus set of a quasiregular map, with D. J. Sixsmith, Geom. Ded., 214 (2021), 241-249.
42. On uniformly disconnected Julia sets, with V. Vellis, Math. Z., 299 (2021), 853-866.
41. On Julia limiting directions in higher dimensions, Comp. Meth. Func. Th., 24 (2021), 587-603.
40. Quasiconformality and hyperbolic skew, with C. Ackermann, Math. Proc. Cam. Phil. Soc., 171, no.3 (2021), 449-466.
39. A complete realization of the orbits of generalized derivatives of quasiregular mappings, with J. Pratscher, J. Geom. Anal., 31 (2021), 4447-4491.
38. On locally quasiconformal Teichmueller spaces, with Zhou Zemin, Manuscripta Math., 165 (2021), 105-119.
37. Spiders' webs of doughnuts, with D. Stoertz, Rev. Mat. Ibero., 37, no.1 (2021), 161-176.
36. Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings, with D. Macclure, J. Anal. Math., 141 (2020), 483-520.
35. Attractor sets and Julia sets in low dimensions, Conform. Geom. Dyn., 23 (2019), 117-129.
34. On simultaneous linearization, with D. Macclure, Aeq. Math., 93 (2019), 1009-1037.
33. The orbits of generalized derivatives, with B. Wallis, Ann. Acad. Sci. Fenn., 44 (2019), 485-495.
32. Quasiregular semigroups with examples, Discrete Contin. Dyn. Syst., 39(4) (2019), 2157-2172.
31. Epicycloids and Blaschke products, with C. Cao and Z. Ye, J. Diff. Eq. Appl., 23, no.9 (2017), 1584-1596.
30. On infinitesimal Strebel points, Kodai Math. J., 40, no.3 (2017), 553-561.
29. On the infinitesimal space of uqr mappings, with D. Macclure, J. Waterman and S. Wesley, J. Analysis, Volume 24, Issue 1 (2016), 67-81.
28. Fixed curves near fixed points, Illinois J. Math, 59, no.1 (2016), 189-217.
27. Superattracting fixed points of quasiregular mappings, with D. A. Nicks, Ergodic Theory and Dynamical Systems, 36, no.3, (2016), 781-793.
26. Dynamics of mappings with constant complex dilatation, with R. Fryer, Ergodic Theory and Dynamical Systems, 36, no.2 (2016), 514-549.
25. Unicritical Blaschke products and domains of ellipticity, Qual. Th. Dyn. Sys., 14, no.1 (2015), 25-38.
24. On quasiregular linearizers, with D. Macclure, Comp. Meth. Func. Th., 15, no.2 (2015), 263-276.
23. Julia sets and wild Cantor sets, with J.-M. Wu, Geom. Ded., 174, no.1 (2015), 169-176.
22. Poincare linearizers in higher dimensions, Proc. Amer. Math. Soc., 143 (2015), 2543-2557.
21. The fast escaping set for quasiregular mappings, with W. Bergweiler and D. Drasin, Anal. Math. Phys. 4 (2014), 83-98.
20. The Julia set and the fast escaping set of a quasiregular mapping, with W. Bergweiler and D. A. Nicks, Comp. Meth. Func. Th., 14, no.2 (2014), 209-218.
19. The moduli space of Riemann surfaces of large genus, with J. Kahn and V. Markovic, Geometric and Functional Analysis, 23, no.3 (2013), 867-887.
18. Chaotic dynamics of a quasiregular sine mapping, with D. A. Nicks, J.Difference Equ. Appl., 19, no.8 (2013), 1353-1360.
17. On Boettcher coordinates and quasiregular maps, with R. Fryer, Contemp. Math., 575, volume title: Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces (2012), 53-76.
16. Decomposing diffeomorphisms of the sphere, with V. Markovic, Bull. London Math. Soc., 44, no.3 (2012), 599-609.
15. Iteration of quasiregular tangent functions in three dimensions, with D. A. Nicks, Conform. Geom. Dyn., 16 (2012), 1-21.
14. Julia sets of uniformly quasiregular mappings are uniformly perfect, with D. A. Nicks, Math. Proc. Cam. Phil. Soc., 151, no.3 (2011), 541-550.
13. Quasiregular dynamics on the n-sphere, with D. A. Nicks, Ergodic Theory and Dynamical Systems, 31 (2011), 23-31.
12. Quasiregular mappings of polynomial type in R^2, with D. Goodman, Conform. Geom. Dyn., 14 (2010), 322-336.
11. On Asymptotic Teichmueller space, Trans. Amer. Math. Soc., 362 (2010), 2507-2523.
10. Nonvanishing derivatives and the MacLane class A, with J. K. Langley and J. Meyer, Illinois J. Math., 53 (2009) 379-390.
9. Integer points of analytic functions in a half-plane, with J. K. Langley, Proc. Edin. Math. Soc., 52, no.3 (2009) 619-630.
8. Meromorphic compositions and target functions, with J. K. Langley, Ann. Acad. Sci. Fenn., 34 (2009), 615-636.
7. Slowly growing meromorphic functions and the zeros of differences, with J. K. Langley and J. Meyer, Math. Proc. R. Ir. Acad., 109A(2) (2009), 147-154.
6. Infinite dimensional Teichmüller spaces, with V. Markovic. A survey article in the Handbook of Teichmüller theory, Volume 2 by the European Mathematical Society.
5. The escaping set of a quasiregular mapping, with W. Bergweiler, J. K. Langley and J. Meyer, Proc. Amer. Math. Soc., 137 (2009) 641-651.
4. On Bank-Laine functions, Computational Methods and Function Theory, 9, (2009) 227-238.
3. Gaussian integer points of functions analytic in a half-plane, Math. Proc. Cam. Phil. Soc., 145, no.2 (2008), 257-272.
2. Local rigidity of infinite dimensional Teichmueller spaces, J. London Math. Soc., (2) 74 (2006) 26-40.
1. On the zeros of functions in the Bers space, with V. Markovic, Publications de l'Institut Mathématique, Nouvelle série, tome 75, (89) (2004) 185-197. (Note that the proof of Theorem 4.5 can charitably be called unclear. Refer to my thesis below, pages 114-120, for a complete proof. Section 3.5 of my thesis gives a different proof of Theorem 4.5 using Teichmüller theory)
Refereed Conference Proceedings
Sassman, P., Rupnow, R., & Fletcher, A. (2025). Mathematicians’ values and norms related to algorithms, Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education (pp. 101–108).
Rupnow, R., Fletcher, A., & Sassman, P. (2025). Norms and values upheld by different mathematical activities: Proving, defining, and algorithmatizing, Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education (pp. 1–9).
Book
Quasiconformal Maps and Teichmüller Theory, A. Fletcher and V. Markovic, Oxford Graduate Texts in Mathematics 11. Oxford University Press (2007).
Ph.D. Thesis
Local Rigidity of Infinite Dimensional Teichmueller Spaces, University of Warwick, 2006.