Selected Publications

Here we list some of the most important publications of our group, including some former group members with their work carried out in Bremen.

Parameter spaces and the Mandelbrot set

  • Dierk Schleicher: Rational Parameter Rays of the Mandelbrot Set. Astérisque 261 (2000), 409-447. (article)
  • Hiroyuki Inou, Sabyasachi Mukherjee: Non-landing parameter rays of the multicorns. Inventiones Mathematicae, 202 (2015), 1-25.  (arxiv)
  • Vladlen Timorin: Topological regluing of rational functions. Inventiones Mathematicae, 179 3 (2010), 461-506. (arxiv)

Newton dynamics 

  • John Hubbard, Dierk Schleicher and Scott Sutherland: How to find all roots of complex polynomials with Newton’s method. Inventiones Mathematicae, 146 (2001), 1-33. (article)
  • Russell Lodge, Yauhen “Zhenya” Mikulich and Dierk Schleicher: A classification of postcritically finite Newton maps. Submitted. (arxiv)
  • Khudoyor Mamayusupov: On postcritically minimal Newton maps, (2015). (thesis)
  • Dierk Schleicher, Robin Stoll: Newton's method in practice: finding all roots of polynomials of degree one million efficiently. Journal of Theoretical Computer Science (to appear). (arxiv)
  • Todor Bilarev, Magnus Aspenberg, and Dierk Schleicher: On the speed of convergence of Newton's method for complex polynomials. Mathematics of Computation 85 298 (2016), 693-705. (arxiv)

Transcendental dynamics/Hausdorff dimension

  • Günter Rottenfußer, Johannes Rückert, Lasse Rempe, and Dierk Schleicher: Dynamic rays of bounded-type entire functions. Annals of Mathematics, 173 1 (2011), 77-125. (arxiv)
  • Lasse Rempe and Dierk Schleicher: Bifurcations in the space of exponential maps. Inventiones Mathematicae 175 (2009), 103-135. (arxiv)
  • Dierk Schleicher: The dynamical fine structure of iterated cosine maps and a dimension paradox. Duke Mathematics Journal 136 2 (2007), 343-356. (arxiv)
  • Dierk Schleicher: Hausdorff dimension, its properties, and its surprises. American Mathematical Monthly, 114 6 (2007), 509-528. (arxiv)

Thurston theory

  • John Hubbard and Dierk Schleicher: The spider algorithm. Complex dynamical systems, Amer. Math. Soc. (1994), 155-180. (article)
  • John Hubbard, Dierk Schleicher, and Mitsuhiro Shishikura: Exponential Thurston maps and limits of quadratic differentials. Journal of the American Mathematical Society, 22 (2009), 77-117. (article)
  • Nikita Selinger: Thurston’s pullback map on the augmented Teichmüller space and applications. Inventiones Mathematicae, 189 (2012), 111-142. (arxiv)
  • Daniel Meyer: Invariant Peano curves of expanding Thurston maps. Acta Math. 210 1 (2013), 95-171. (arxiv)

Iterated monodromy groups

  • Volodymyr Nekrashevych: Self-similar groups. Mathematical Surveys and Monographs, vol. 117, American Mathematical Society (2005).
  • Russell Lodge: Boundary values of the Thurston pullback map, Conform. Geom. 17 (2013), 77-118. (arxiv)
  • Laurent Bartholdi, Dzmitry Dudko: Algorithmic aspects of branched coverings. (arxiv)

Symbolic dynamics and core entropy

  • Alexander Blokh, Doug Childers, Genadi Levin, Lex Oversteegen, and Dierk Schleicher: An extended Fatou–Shishikura inequality and wandering branch continua for polynomials. Advances in Mathematics 288 (2016), 1121-1174. (arxiv)

 

Books and edited volumes

  • Dierk Schleicher (ed.): Complex Dynamics: Friends and Families. Contributors include William Thurston, Mikhail Lyubich, Mitsuhiro Shishikura, John Milnor, and others. A.K. Peters (2009), 650pp.
  • Dierk Schleicher and Malte Lackmann (ed.): An Invitation to Mathematics. Contributors include Béla Bollobás, Timothy Gowers, László Lovász, Stanislav Smirnov, Terence Tao, Nick Trefethen, Jean-Christophe Yoccoz, Günter Ziegler. Springer Verlag (2011), 220pp.
    German translation: Eine Einladung in die Mathematik. Springer Verlag (2012), 228pp. (Chinese translation in preparation).
  • Dierk Schleicher and Sergei Tabachnikov (guest editors), “Special issue of the American Mathematical Monthly”, Vol. 120 No 3 (2013). Contributors include John Conway, Etienne Ghys, Tadashi Tokieda, Don Zagier.
  • Hans-Dietrich Gronau (ed.), Hanns-Heinrich Langmann (ed.), Dierk Schleicher (ed.): 50th IMO - 50 Years of International Mathematical Olympiads. Springer (2011). This is the official report of the 50th International Mathematical Olympiad IMO 2009 in Bremen,Germany, including historical information on the first 50 IMOs
  • Anke Allner and Dierk Schleicher, “The 50th International Mathematical Olympiad”, 80pp (2011). A lively publication with many pictures, stories, quotations from participants, organizers, and guests at the IMO. (Self-published; available on demand.)