Correlations for pairs of periodic trajectories for open billiards

In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiards similar to those established by Pollicott and Sharp for closed geodesics on negatively curved compact surfaces. The first of these estimates holds for general open billiards in any dimension. The more intricate second estimate is established for open billiards satisfying the so called Dolgopyat type estimates. This class of billiards includes all open billiards in the plane and open billiards in $\R^N, N \geq 3$ satisfying some additional conditions

A Consociational Compromise? Constitutional Evolution in Spain and Catalonia

This chapter examines the prospects of a consociational compromise in Spain and Catalonia as a response to the protracted constitutional stalemate between the two governments. While Spain’s transition to democracy in the late 1970s had a clear consociational tinge, it has since evolved toward the entrenchment of a majoritarian and mononational interpretation of the state, hostile to its plurinational reality and to minority nationalist aspirations in territories like Catalonia. Hitherto, no institutional resolution has been found to satisfy the demands of both sides. This chapter argues that consociational philosophy has much to offer to Spain and Catalonia. While a more consensual approach to politics is crucial to thawing the frosty relations between the pro- and anti-independence sides, the development of a fully-fledged consociational system has yet to gain much traction