| dc.rights.license | CC-BY-NC-ND | |
| dc.contributor.advisor | Hlushchanka, Mikhail | |
| dc.contributor.author | Staikos, Kostas | |
| dc.date.accessioned | 2023-08-25T00:00:54Z | |
| dc.date.available | 2023-08-25T00:00:54Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/44777 | |
| dc.description.abstract | We study several examples of self-similar groups of subexponential growth: the (generalized) Grigorchuk
groups and the kneading automata groups induced by the sequences 1(10), 11(0) and 0(011). According
to Nekrashevych, the last three groups appear as iterated monodromy groups for some complex post-critically
finite quadratic polynomials. In particular, they support Nekrashevych’s conjecture on the intermediate
growth of iterated monodromy groups.
For each of the cases we implement the method of incompressible elements. We conclude that the set of
incompressible elements shares a common trait for all examples: the automaton described by the alternating
patterns of incompressible elements consists of disjoint circles. | |
| dc.description.sponsorship | Utrecht University | |
| dc.language.iso | EN | |
| dc.subject | In the project, we study the growth of iterated monodromy groups, which are self-similar groups naturally associated with postcritically-finite rational maps. Nekrashevych has claimed that the iterated monodromy groups of quadratic, non-renormalizable polynomials with preperiodic critical orbit have intermediate growth. Even though this conjecture seems far from being proven, we give concrete examples which support an affirmative answer to this statement. | |
| dc.title | On self-similar groups of intermediate growth | |
| dc.type.content | Master Thesis | |
| dc.rights.accessrights | Open Access | |
| dc.subject.courseuu | Mathematical Sciences | |
| dc.thesis.id | 22658 | |
