The present book is the first one in the new subject area of non-integrable Hamiltonian partial differential equations, using the approach of analysis and geometry rather than algebra to study the equations. The book will be an invaluable source of information for postgraduate mathematics students and researchers working in analysis as well as for theoretical physicists interested in the topic.

This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier-Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) - proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.

The "Dynamical Systems Semester" took place at the Euler International Mathematical Institute in St. Petersburg, Russia, in the autumn of 1991. There were two workshops, October 14-25 and November 18-29, with more than 60 participants giving 70 talks. The titles of all talks are given at the end of this volume. Here we included 22 papers prepared by the authors especially for this volume, while the material of the other talks are published elsewhere. The semester was sponsored by the Soviet Academy of Sciences and UN ESCO. Since the new building of the Euler Institute was not ready at that moment, the sessions were held in the old building of the Steklov Mathemati cal Institute in the very center of St. Petersburg. Members of the staff of the Euler Institute were doing their best to organize properly the normal processing of the conference-not a simple task at that time because of the complications in the political and economical life in Russia just between the coup d'etat in August and the dismantling of the Soviet Union in December. We are thankful to all of them."

This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants, and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.

Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many applications to physics and astronomy. Other natural small divisor problems arise considering circle diffeomorphisms or quasiperiodic Schroedinger operators. In this volume Hakan Eliasson, Sergei Kuksin and Jean-Christophe Yoccoz illustrate the most recent developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) has been included.

The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr-dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.

Studienarbeit aus dem Jahr 2013 im Fachbereich Jura - Zivilrecht / Handelsrecht, Gesellschaftsrecht, Kartellrecht, Wirtschaftsrecht, Note: 1,7, Universitat Hamburg (Fakultat fur Wirtschaft- und Sozialwissenschaften), Veranstaltung: Offentliches Wirtschaftsrecht, Sprache: Deutsch, Abstract: Prostitution - das alteste Gewerbe der Welt" ist seit dem Inkrafttreten des neuen Prostitutionsgesetzes (ProstG) rechtlich geregelt und im Gesetz verankert. Das Gesetz gilt seit dem 1. Januar 2002. Das Ziel des Gesetzes ist es, den Prostituierten mehr Rechte und soziale Sicherheit zu geben . In der Bundesrepublik Deutschland gehen etwa 400 000 Personen dem Beruf der Prostituierten nach. Es sind uberwiegend Frauen. Taglich nehmen uber eine Million Manner Ihre Dienste in Anspruch . Der jahrliche Umsatz belauft sich in Deutschland auf bis zu 6,4 Mrd. Euro. Der Anteil der Prostitution in Hausern wie Bordellen, Bars, Clubs, sonstige Gaststatten betragt 64%. Diejenigen, die auf der Strasse arbeiten, sind mit 24% vertreten. In die Kategorie Ruf- und Begleitdienst fallen 12%. Doch Prostitution, wie zum Beispiel Strassenprostitution, ist nicht immer fur Aussenstehende sichtbar. Hierbei sprechen die Prostituierten ihre Kunden direkt auf der Strasse an. Nach einem Gesprach wird entweder ins Stundenhotel oder ins Auto gegangen. Hochhauser und Mehrfamilienhauser konnen als Arbeitsstatte fur Prostituierte dienen, was oft nicht zu erkennen ist. Die Kunden vereinbaren telefonisch ihre Besuche. Hierbei spielen die Zeitungsanzeigen eine grosse Rolle. Findet die Prostitution in einer Gaststatte statt, so dient diese als Kontaktaufnahme zum Freier. Bis zum Jahr 2002 gilt die Prostitution als sittenwidrig im Sinne von 138 BGB. Demnach gelten alle Geschafte, die gegen die guten Sitten verstossen, als nichtig. Unter den guten Sitten ist dabei die in der Gesellschaft vorherrschende Rechts- und Sozialmoral zu verstehen. Als Folge davon gelten die Vertrage als nichtig, die zwischen der Prostituierten und d"