Markov Extensions for Dynamical Systems with Holes: An Application to Expanding Maps of the Interval

We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of conditionally invariant probability measures which are absolutely continuous with respect to Lebesgue measure (abbreviated a.c.c.i.m.). We develop restrictions on the Lebesgue measure of the holes and simple conditions on the dynamics of the tower which ensure existence and uniqueness in a class of Holder continuous densities. We then use these results to study the existence and properties of a.c.c.i.m. for expanding maps of the interval with holes. We obtain the convergence of the a.c.c.i.m. to the SRB measure of the corresponding closed system as the measure of the hole shrinks to zero.Comment: 32 pages. New version contains minor revisions, primarily to clarify introductory Section

The Failures of Litigation as a Tool for the Development of Social Welfare Policy

This article argues that litigation is largely counterproductive to the development of a coherent and feasible social welfare policy and interferes with the constitutionally-derived separation of powers. It describes the proper role of the courts when evaluating government actions and the proper procedures for doing so. It then discusses several cases brought against the New York State Department of Social Services and local governments, arguing that the courts have abandoned their appropriate role, and using these decisions to illustrate its thesis

The Canadian Phillips Curve and Regime Shifting

Phillips curves are generally estimated under the assumption of linearity and parameter constancy. Linear models of inflation, however, have recently been criticized for their poor forecasting performance. The author investigates the linearity and constancy assumptions of a standard reduced-form Phillips curve for Canada using two different techniques: (i) the methodology proposed by Bai and Perron (1998), which allows for an unknown number of breaks at unknown dates, and (ii) a three-regimes Markov-switching regression model. Both methodologies strongly reject the linearity and parameter constancy assumptions. The author finds that the output-inflation relationship does not hold under the current monetary policy of inflation targeting, with its low and stable inflation. Since the inflation-control targets were adopted, inflation expectations appear to be more forward looking and well anchored at 2 per cent, the official target rate. Core inflation exhibits very low persistence and there do not appear to be significant asymmetries in the inflation response to output-gap shocks within regimes. Generalized impulse responses are computed to illustrate some properties of the Markov-switching Phillips curve model.

Hermiticity and the Cohomology Condition in Topological Yang-Mills Theory

The symmetries of the topological Yang-Mills theory are studied in the Hamiltonian formalism and the generators of the twisted N=2 superPoincar\'e algebra are explicitly constructed. Noting that the twisted Lorentz generators do not generate the Lorentz symmetry of the theory, we relate the two by extracting from the latter the twisted version of the internal SU(2) generator. The hermiticity properties of the various generators are also considered throughout, and the boost generators are found to be non-hermitian. We then recover the BRST cohomology condition on physical states from representation theory arguments.Comment: 19 pages, MIT-CTP 223

The Failures of Litigation as a Tool for the Development of Social Welfare Policy

This article argues that litigation is largely counterproductive to the development of a coherent and feasible social welfare policy and interferes with the constitutionally-derived separation of powers. It describes the proper role of the courts when evaluating government actions and the proper procedures for doing so. It then discusses several cases brought against the New York State Department of Social Services and local governments, arguing that the courts have abandoned their appropriate role, and using these decisions to illustrate its thesis

Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas

In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Holder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles.Comment: Final version, to appear in Nonlinearity. Corrected some minor typos from previous versio