Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces

In the present paper, we establish two fixed point theorems for upper semicontinuous multivalued mappings in hyperconvex metric spaces and apply these to study coincidence point problems and minimax problems. (C) 2002 Elsevier Science (USA). All rights reserved.

Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

Pedagogies and critical reflection: key understandings for transformative gender justice

It is widely acknowledged that quality pedagogy is central to improving the educational outcomes of all students. In improving the social and academic outcomes of boys, and more specifically disengaged boys, the productive pedagogies model has been presented as a way forward. In terms of drawing on this model in socially just ways; to facilitate a broadening, rather than reinscribing of boys' narrow constructions of gender identity, this paper illustrates the imperative of teachers interacting with key feminist understandings of masculinity. Organized around the four dimensions of productive pedagogy, the paper draws on ( predominantly Australian-based) seminal work in the sphere of masculinities and schooling to discuss key strategies and initiatives for improving boys' educational outcomes. Against this backdrop, the paper demonstrates the importance of two principle understandings. The first relates to teachers understanding masculinity through feminist lenses, as constructed, regulated and maintained through inequitable social processes and the second relates to teachers understanding pedagogy as critical and transformative practice. These understandings are presented as vital to enabling gender justice.

Some new examples for nonuniqueness of the evolution problem of harmonic maps

We find some new examples to show nonuniquence for the heat flow of harmonic maps where weak solutions satisfy the same monotonicity property.

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Disability focus groups: A strategy for including people with disability in parishes

This paper reports the findings of an exploratory qualitative study examining parish awareness of the need to include individuals with disability in genuine and meaningful ways. Based on the interviews of over thirty persons, including people with disability, parents, parish workers, volunteers and human service workers within church agencies in the Catholic Archdiocese of Brisbane, Australia, the authors devised a process for including individuals in parishes. This process, known as a Disability Focus Group, was then implemented in one parish as a pilot study. The outcomes of the pilot are discussed.