2+1 gravity, chaos and time machines

2+1 gravity for spacetimes with topology RxT^2 has been much studied. We add a description of how to extend these spacetimes across a Cauchy horizon into a region where the torus becomes Lorentzian. The result is a one parameter family of tori given by a geodesic in the "Teichmueller space" of Lorentzian tori. We describe this in detail. We also point out that if the modular group is regarded as part of the gauge group then these spacetimes offer a nice toy model for the dynamics of Bianchi IX models; in the region where the tori are spacelike the dynamics is described exactly by a hyperbolic billiard. On the other hand the modular group acts ergodically on the Teichmueller space of Lorentzian tori

Green regulations in Califorina and Sweden

California and Sweden are both leaders in green regulations and actions. In both there is a substantial political base for environmental regulation, yet the path to regulation in these two political entities is quite different. California emphasizes command and control regulations while Sweden makes heavy use of taxes. We show that both underlying economic factors and the constraints of the larger systems in which these economies are embedded contribute to their choice of control methods

Green regulations in Califorina and Sweden

California and Sweden are both leaders in green regulations and actions. In both there is a substantial political base for environmental regulation, yet the path to regulation in these two political entities is quite different. California emphasizes command and control regulations while Sweden makes heavy use of taxes. We show that both underlying economic factors and the constraints of the larger systems in which these economies are embedded contribute to their choice of control methods.energy policy, environmental aspects, climate change, automobiles, regulations, Agricultural and Resource Economics

Green regulations in Califorina and Sweden

California and Sweden are both leaders in green regulations and actions. In both there is a substantial political base for environmental regulation, yet the path to regulation in these two political entities is quite different. California emphasizes command and control regulations while Sweden makes heavy use of taxes. We show that both underlying economic factors and the constraints of the larger systems in which these economies are embedded contribute to their choice of control methods.energy policy, environmental aspects, climate change, automobiles, regulations