442 research outputs found

    A Fundamental Domain for V_3

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    We describe a fundamental domain for the punctured Riemann surface V3,mV_{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 mm 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 V3V_{3}, and gives indications of a topological model for V3V_{3}, together with the hyperbolic components contained in it.Comment: 120 page

    Counting Hyperbolic Components

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    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

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    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

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    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
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