Dogging Cornwall’s 'secret freaks': Béroul on the limits of European orthodoxy

This piece argues that Béroul's version of the Tristan tale can be read as offering a discreetly veiled view of the sexual, ritual and ontological chaos associated with visions of the Celtic West such as figure in Gerald of Wales' History and Topography of Ireland as well as with accounts of heretical orgies found in continental sources such as Caesarius of Heisterbach. Drawing parallels between the poem’s fictional Cornwall and Gerald’s often hyperbolically lurid accounts of the perversions and peculiarities of Ireland, both religious and sexual, this essay targets the cultural voyeurism in which the world of King Mark appears to veil its kinship with the deviance and hybridity Gerald presents as characteristic of religious life across the Irish Sea. This relation can perhaps helpfully be characterised as a form of cultural 'dogging', the sociology of which is one of the methodological focuses of this paper and which mirrors Béroul's recurring focus on voyeuristic scenarios. Evidently, however, the disavowed investments underlying orthodoxy's voyeuristic fascination with what Gerald describes as the'secret freaks' nature spawns in Ireland also reflect a desire to render unintelligible the logics of othered practices. What gives Béroul’s text an edginess discernible even today is the clear implication that such ‘flawed’ societies operated on their own cultural terms and according to the

A general framework for boundary equilibrium bifurcations of Filippov systems

As parameters are varied a boundary equilibrium bifurcation (BEB) occurs when an equilibrium collides with a discontinuity surface in a piecewise-smooth system of ODEs. Under certain genericity conditions, at a BEB the equilibrium either transitions to a pseudo-equilibrium (on the discontinuity surface) or collides and annihilates with a coexisting pseudo-equilibrium. These two scenarios are distinguished by the sign of a certain inner product. Here it is shown that this sign can be determined from the number of unstable directions associated with the two equilibria by using techniques developed by Feigin. A new normal form is proposed for BEBs in systems of any number of dimensions. The normal form involves a companion matrix, as does the leading order sliding dynamics, and so the connection to the stability of the equilibria is explicit. In two dimensions the parameters of the normal form distinguish, in a simple way, the eight topologically distinct cases for the generic local dynamics at a BEB. A numerical exploration in three dimensions reveals that BEBs can create multiple attractors and chaotic attractors, and that the equilibrium at the BEB can be unstable even if both equilibria are stable. The developments presented here stem from seemingly unutilised similarities between BEBs in discontinuous systems (specifically Filippov systems as studied here) and BEBs in continuous systems for which analogous results are, to date, more advanced

A Panel Test of Purchasing Power Parity Under the Null of Stationarity

Purchasing Power Parity (PPP) is tested using a sample of real exchange rate data for twelve European countries. Acknowledging that Augmented Dickey Fuller tests have low power, we apply a Panel test that considers the null of stationarity and corrects for serial dependence using a non-parametric kernel based method

Scaling laws for large numbers of coexisting attracting periodic solutions in the border-collision normal form

A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsmooth. For the border-collision normal form in two dimensions, a codimension-three scenario was described in previous work at which the map has a saddle-type periodic solution and an infinite sequence of stable periodic solutions that limit to a homoclinic orbit of the saddle-type solution. This paper introduces an alternate scenario of the same map at which there is an infinite sequence of stable periodic solutions due to the presence of a repeated unit eigenvalue in the linearization of some iterate of the map. It is shown that this scenario is codimension-four and that the sequence of periodic solutions is unbounded, aligning with eigenvectors corresponding to the unit eigenvalue. Arbitrarily many attracting periodic solutions coexist near either scenario. It is shown that if $K$ denotes the number of attracting periodic solutions, and $\varepsilon$ denotes the distance in parameter space from one of the two scenarios, then in the codimension-three case $\varepsilon$ scales with $\lambda^{-K}$, where $\lambda > 1$ denotes the unstable stability multiplier associated with the saddle-type periodic solution, and in the codimension-four case $\varepsilon$ scales with $K^{-2}$. Since $K^{-2}$ decays significantly slower than $\lambda^{-K}$, large numbers of attracting periodic solutions coexist in open regions of parameter space extending substantially further from the codimension-four scenarios than the codimension-three scenarios.Comment: 37 pages, 5 figures, submitted to: Int. J. Bifurcation Chao