On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number

From a simple observation about a construction of Thurston, we derive several interesting facts about subgroups of the mapping class group generated by two positive multi-twists. In particular, we identify all configurations of curves for which the corresponding groups fail to be free, and show that a subset of these determine the same set of Teichmueller curves as the non-obtuse lattice triangles which were classified by Kenyon, Smillie, and Puchta. We also identify a pseudo-Anosov automorphism whose dilatation is Lehmer's number, and show that this is minimal for the groups under consideration. In addition, we describe a connection to work of McMullen on Coxeter groups and related work of Hironaka on a construction of an interesting class of fibered links.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper36.abs.htm

Retribution and the Experience of Punishment

In a prior article, we argued that punishment theorists need to take into account the counterintuitive findings from hedonic psychology about how offenders typically experience punishment. Punishment generally involves the imposition of negative experience. The reason that greater fines and prison sentences constitute more severe punishments than lesser ones is, in large part, that they are assumed to impose greater negative experience. Hedonic adaptation reduces that difference in negative experience, thereby undermining efforts to achieve proportionality in punishment. Anyone who values punishing more serious crimes more severely than less serious crimes by an appropriate amount - as virtually everyone does - must therefore confront the implications of hedonic adaptation. Moreover, the unadaptable negativity of post-prison life which is caused by the experience of imprisonment results in punishments that go on far longer than is typically assumed. Objectivist retributive theories that fail to incorporate these facts risk creating grossly excessive punishments. Certain retributivists have disputed the claim that adaptation is important to punishment theory, but their arguments are unavailing

Happiness and Punishment

This article continues our project to apply groundbreaking new literature on the behavioral psychology of human happiness to some of the most deeply analyzed questions in law. Here we explain that the new psychological understandings of happiness interact in startling ways with the leading theories of criminal punishment. Punishment theorists, both retributivist and utilitarian, have failed to account for human beings\u27 ability to adapt to changed circumstances, including fines and (surprisingly) imprisonment. At the same time, these theorists have largely ignored the severe hedonic losses brought about by the post-prison social and economic deprivations (unemployment, divorce, and disease) caused by even short periods of incarceration. These twin phenomena significantly disrupt efforts to attain proportionality between crime and punishment and to achieve effective marginal deterrence. Hedonic psychology thus threatens to upend conventional conceptions of punishment and requires retributivists and utilitarians to find novel methods of calibrating traditional punitive sanctions if they are to maintain the foundations upon which punishment theory rests

Ergodic directions for billiards in a strip with periodically located obstacles

We study the size of the set of ergodic directions for the directional billiard flows on the infinite band $\R\times [0,h]$ with periodically placed linear barriers of length $0<\lambda<h$. We prove that the set of ergodic directions is always uncountable. Moreover, if $\lambda/h\in(0,1)$ is rational the Hausdorff dimension of the set of ergodic directions is greater than 1/2. In both cases (rational and irrational) we construct explicitly some sets of ergodic directions.Comment: The article is complementary to arXiv:1109.458