A Fundamental Domain for V_3

We describe a fundamental domain for the punctured Riemann surface $V_{3,m}$ which parametrises (up to M\"obius conjugacy) the set of quadratic rational maps with numbered critical points, such that the first critical point has period three, and such that the second critical point is not mapped in $m$ iterates or less to the periodic orbit of the first. This gives, in turn, a description, up to topological conjugacy, of all dynamics in all type III hyperbolic components in $V_{3}$, and gives indications of a topological model for $V_{3}$, together with the hyperbolic components contained in it.Comment: 120 page

Counting Hyperbolic Components

We give formulas for the numbers of type II and type IV hyperbolic components in the space of quadratic rational maps, for all fixed periods of attractive cycles

An exploration of the development of academic identity in a School of Education

This paper explores the complex processes involved in the self-construction of academic identity in a UK School of Education. Building on seminal literature in this field and drawing on the research of four academics, it begins by discussing teacher educators’ varying perceptions of the need to re-configure their identity to meet the expectations of a twenty-first-century higher education workforce. The article proposes the formation of this identity to be a dynamic, career-long process. Diverse scaffolds for the development process are proposed, including opportunities for new teacher educators to be apprenticed into an aca- demic role, the centrality of communities of practice and the importance of the 15 supported development of academic skills such as writing for publication.Peer reviewe

Persistent Markov partitions for rational maps

A construction is given of Markov partitions for some rational maps, which persist over regions of parameter space, not confined to single hyperbolic components. The set on which the Markov partitions exists, and its boundary, are analyse