No elliptic islands for the universal area-preserving map

A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} to prove the existence of a \textit{universal area-preserving map}, a map with hyperbolic orbits of all binary periods. The existence of a horseshoe, with positive Hausdorff dimension, in its domain was demonstrated in \cite{GJ1}. In this paper the coexistence problem is studied, and a computer-aided proof is given that no elliptic islands with period less than 20 exist in the domain. It is also shown that less than 1.5% of the measure of the domain consists of elliptic islands. This is proven by showing that the measure of initial conditions that escape to infinity is at least 98.5% of the measure of the domain, and we conjecture that the escaping set has full measure. This is highly unexpected, since generically it is believed that for conservative systems hyperbolicity and ellipticity coexist

U.S. Survey of Services Provided by Adolescent Pregnancy Programs, 1980

This study, sponsored by the Office of Adolescent Pregnancy Programs, involved a nationwide survey of adolescent pregnancy projects. Part of a national investigation of the problems associated with adolescent pregnancy and of methods for improving services to those directly affected by teenage childbearing, the study sought to "delineate, identify, describe, and evaluate existing programs at the federal, state, and local levels associated with the problem of adolescent pregnancy and adolescent parents". To these ends, data were obtained regarding (1) the general characteristics of the program (e.g., location, catchment area, sponsorship, age of program , and age-range of clients), (2) the types of services offered by the program and the mode of provision of those services, and (3) key administrative features of the project, including demographic data regarding the clients served, program monitoring and evaluation procedures, and sources of progra m funding