Dynamics of shear homeomorphisms of tori and the Bestvina-Handel algorithm

Sharkovskii proved that the existence of a periodic orbit in a one-dimensional dynamical system implies existence of infinitely many periodic orbits. We obtain an analog of Sharkovskii's theorem for periodic orbits of shear homeomorphisms of the torus. This is done by obtaining a dynamical order relation on the set of simple orbits and simple pairs. We then use this order relation for a global analysis for a quantum chaotic physical system called the kicked accelerated particle.Comment: 31 pages, 24 figures, to appear in Topological Methods in Nonlinear Analysi

Looking for GRB progenitors

Using stellar binary population synthesis code we calculate the production rates and lifetimes of several types of possible GRB progenitors. We consider mergers of double neutron stars, black hole neutron stars, black hole white dwarfs and helium star mergers. We calibrate the results with the measured star formation rate history. We discuss the viability of each GRB model, and alternatively assuming that all bursts are connected with one model we constrain the required collimation of GRBs. We also show the importance of widely used evolutionary parameters on the merger rates of calculated binary populations.Comment: 5 pages, 2 figures, Latex with aipproc.sty, Proc. of the 5th Huntsville Gamma Ray Burst Symposium, Oct. 1999, ed. R.M. Kippen, AI

The reformation of place:religion, space and power

In this chapter I reflect on the role played by the Protestant Reformation in shaping the western experience of place. First I examine the idea that the Reformation helps to effect a shift from absolute to abstract space, or from place to space, by purging the landscape of the dramatic highs and lows of spiritual intensity characteristic of Catholicism. I further explore this claim by situating this development within the longue durée of western religious history, a succession of distinctive ‘orderings of the sacred’ which together I term the ‘long arc of monotheism’. Second, however, I argue that the Reformation did not automatically lead to the hypermodern dissolution of space and the emergence of non-places but, more positively, constituted a final overcoming of archaic religion, and the possibility of a new experience of space and place. Thirdly I thus argue for a distinctive mode of placing, one suspended between the archaic and the modern, between belonging and not belonging

From the Anthropocene epoch to a new Axial Age:using theory fictions to explore geo-spiritual futures

In this chapter, Szerszynski discusses how he used a series of linked ‘theory-fictions’ to explore possible futures for religion in a new geological epoch, using the notion of a possible ‘Second Axial Age’ based on a radically different metaphysics. Szerszynski first explores Karl Jaspers’ idea of the ‘Axial Age’. In a 1949 book, Jaspers proposed that around the middle of the first millennium BCE a revolutionary shift occurred in cultures across Eurasia, as spiritual teachers arose who promoted ideas of a cosmological gap between the mundane and transcendent realms, and a distinction between relative local cultures and universal truths. Szerszynski argues that any understanding of paths to the Anthropocene has to take account of the emergence of Axial cultures, but cautions that this has to be done with care. He then introduces the concept of theory fictions and summarizes his own use of the genre: in three pieces all set in a fictional future in which Earth religions and cultures undergo a Second Axial Age in response to the encounter with extraterrestrial cultures and a growing understanding of the interconnectedness of living and non-living systems. Szerszynski explains how he develops in some detail one particular example of this imagined cultural shift, an offshoot of Tibetan Buddhism: Mangalayana or ‘Mars-Vehicle’ Buddhism, involving a form of geological mysticism and a new understanding of cosmic human destiny. Critically exploring contemporary claims that a Second Axial Age is emerging in the twenty-first century, Szerszynski points out, that the Second Axial Age described in his own theory-fictions is not a renewal of First-Axial-Age themes of transcendence and universality, but a turning towards a radically new metaphysics. Szerszynski finally develops the idea of ‘sacred work’. In his fictions, the activity of Martian settlers in making the red planet habitable is not understood as a secular, technological act of humanization but as a spiritual vocation involving the balancing of landscape energies and forces in the tradition of Tibetan geomancy. He concludes by suggesting that such experimental fusions between literary genres can help us to understand what it might mean to escape the limitations of First-Axial-Age thinking, and imagine different futures for religion in the Anthropocene