Quasi-periodic motions in dynamical systems. Review of a renormalisation group approach

Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the so-called small divisor problem. In this paper we review a method recently introduced to deal with such a problem, based on renormalisation group ideas and multiscale techniques. Applications to both quasi-integrable Hamiltonian systems (KAM theory) and non-Hamiltonian dissipative systems are discussed. The method is also suited to situations in which the perturbation series diverges and a resummation procedure can be envisaged, leading to a solution which is not analytic in the perturbation parameter: we consider explicitly examples of solutions which are only infinitely differentiable in the perturbation parameter, or even defined on a Cantor set.Comment: 36 pages, 8 figures, review articl

Anticoagulant therapy with fondaparinux in a liver transplant patient with thrombosis and liver fibrosis: a case report

The treatment with fondaparinux is the effective and safe anticoagulant therapy in liver transplant patient on immunosuppressive therapy with arterial thrombosis, and it seems able to reduce liver fibrosis. Although this treatment is not generalizable, further prospective large studies need to confirm this case report

Bryuno Function and the Standard Map

For the standard map the homotopically non-trivial invariant curves of rotation number satisfying the Bryuno condition are shown to be analytic in the perturbative parameter, provided the latter is small enough. The radius of convergence of the Lindstedt series -- sometimes called critical function of the standard map -- is studied and the relation with the Bryuno function is derived: the logarithm of the radius of convergence plus twice the Bryuno function is proved to be bounded (from below and from above) uniformily in the rotation number.Comment: 120 K, Latex, 33 page

Population Geography Perspectives on the Central Asian Republics

Since the fall of the iron curtain, research on population issues in Central Asia, with the exception of migration, has lost ground in the academia, and little is known about the geographical dimensions of population issues in this region beyond the findings of the handful of studies carried out under the auspices of international organisations. Therefore, the purpose of this paper is to outline the main traits of the population geography of the Central Asian Republics of Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan and Uzbekistan. The report investigates the geographical characteristics of the countries’ vital statistics, as well as of other significant demographic indicators, such as the age structure, dependency ratio and infant mortality. Additionally, the report attempts to establish whether particular regional and local demographies show inter-linkages with the specific socio-economic and/or cultural settings that they are embedded in. The report uses the systematic collection and analysis of data from statistical sources as its main method. Most of the statistical materials derive from the national statistical authorities of the USSR and its successor states, although additional and complementary data was collected from the US Bureau of Census’ international database web resource. The use of such data involves substantial methodological and interpretative difficulties, which this report discusses in detail. Applying a three-scale geographical approach on the study of the Central Asian Republics’ population development, this report demonstrates that there are significant variations in the territoriality of these countries’ demographies. The variations are indeed striking, and suggest that the five states will face distinctly spatially differentiated challenges with regard to the volume and type of healthcare that will be required, the nature of the demand for housing, social and cultural services, and the structure of the labour market, just to name a few examples. These challenges should be taken into greater consideration by policy-makers and other stakeholders, along with matters of more immediate concern, such as the poor health infrastructure and sanitary situation, the high rate of poverty, environmental degradation, and the economic and political instability in the southern regions, most recently epitomized by the Ferghana valley-based “tulip” revolution in Kyrgyzstan and the violent riots in the Uzbek city of Andijan.Population Geography Perspectives; Central Asian Republics