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

Fluctuations of the Unruh Temperature

Using the influence functional formalism, the problem of an accelerating detector in the presence of a scalar field in its ground state is considered in Minkowski space. As is known since the work of Unruh, to a quantum mechanical detector following a definite, classical acceleration, the field appears to be thermally excited. We relax the requirement of perfect classicality for the trajectory and substitute it with one of {\it derived} classicality through the criteria of decoherence. The ensuing fluctuations in temperature are then related with the time and the amplitude of excitation in the detector's internal degree of freedom.Comment: LATEX, 12 pages + 2 figures (available upon request) MIT-CTP 234

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