The Periodical Cicada

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Periodicity and Quasi-Periodicity for Super-Integrable Hamiltonian Systems

Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All finite trajectories are quasi-periodical; they become truly periodical if a commensurability condition is imposed on an angular momentum component

Review of periodical articles

[First Paragraph] There is only one true city, wrote St Augustine, and it is not of this world. The pessimistic Christian response to the fall of Rome in AD 410, epitomized in Augustine's City of God, affected the development of the later medieval city to a degree which has yet, even now, to be fully appreciated. In the Christian city of the Middle Ages the divinity was normally confined to the sanctuaries of his churches, whose topographical prominence and harmonious proportions made manifest an otherwise hidden spiritual order. Outside the cloister gates, disorder reigned: a general lack of planning revealed the meaninglessness of the outward, secular life. This dichotomy between an inner world of spirit and a public world of transient matter was embodied in the recurrent tensions between spiritual and secular space which ran as a motif throughout the history of medieval towns. Modern studies which have emphasized (not, of course, without reason) the secular political and economic power of ecclesiastical institutions in the medieval city have perhaps distracted attention unduly from the real differences of ethos which, within the town, distinguished religious space from that of the surrounding lay world

Review of periodical articles

One of the attractions of medieval urban history is the fact that major conceptual problems in the field continue to be debated. In a stimulating review article by J.H. Mundy, ’Philip Jones and the medieval Italian city-state‘, J. of European Economic History, 28 (1999), 185–200, one distinguished scholar is taxed for holding views now dismissed by some, but of which he is by no means a unique surviving representative. One of these views assumes a clear distinction between the antique city, supposedly a bureaucratic centre with limited economic functions, and the medieval city, as the home of industrious artisans and nascent capitalism. The image of the non-profit-making ancient town may be overly indebted to the nature of the literary sources and to the prevalent interests of classicists; but, although many would now agree that both the elements in the above equation need qualifying, a more focused comparison is presently lacking, and a fine book is still waiting to be written on the transition from the ancient world to the middle ages in urban history