caa a22 4500 445884436 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10711-010-9499-2 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9499-2 Blocks of monodromy groups in complex dynamics [Elektronische Daten] [Rafe Jones, Han Peters] Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. The Author(s), 2010 Iterated monodromy groups nationallicence Complex dynamics nationallicence Polynomial iteration nationallicence Post-critically finite polynomials nationallicence Conservative polynomials nationallicence Constant weighted sum of iterates nationallicence Jones Rafe Department of Mathematics and CS, College of the Holy Cross, Worcester, MA, USA aut Peters Han Department of Mathematics, University of Amsterdam, Amsterdam, Netherlands aut Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 137-150 0046-5755 150:1<137 2011 150 10711 https://doi.org/10.1007/s10711-010-9499-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9499-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jones Rafe Department of Mathematics and CS, College of the Holy Cross, Worcester, MA, USA aut NATIONALLICENCE 700 1- Peters Han Department of Mathematics, University of Amsterdam, Amsterdam, Netherlands aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 137-150 0046-5755 150:1<137 2011 150 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer