Nicolas Rouche – författare

This monograph is a collective work. The names appear­ ing on the front cover are those of the people who worked on every chapter. But the contributions of others were also very important: C. Risito for Chapters I, II and IV, K. Peiffer for III, IV, VI, IX R. J. Ballieu for I and IX, Dang Chau Phien for VI and IX, J. L. Corne for VII and VIII. The idea of writing this book originated in a seminar held at the University of Louvain during the academic year 1971-72. Two years later, a first draft was completed. However, it was unsatisfactory mainly because it was ex­ ce~sively abstract and lacked examples. It was then decided to write it again, taking advantage of -some remarks of the students to whom it had been partly addressed. The actual text is this second version. The subject matter is stability theory in the general setting of ordinary differential equations using what is known as Liapunov's direct or second method. We concentrate our efforts on this method, not because we underrate those which appear more powerful in some circumstances, but because it is important enough, along with its modern developments, to justify the writing of an up-to-date monograph. Also excellent books exist concerning the other methods, as for example R. Bellman [1953] and W. A. Coppel [1965].

This monograph is a collective work. The names appear­ ing on the front cover are those of the people who worked on every chapter. But the contributions of others were also very important: C. Risito for Chapters I, II and IV, K. Peiffer for III, IV, VI, IX R. J. Ballieu for I and IX, Dang Chau Phien for VI and IX, J. L. Corne for VII and VIII. The idea of writing this book originated in a seminar held at the University of Louvain during the academic year 1971-72. Two years later, a first draft was completed. However, it was unsatisfactory mainly because it was ex­ ce~sively abstract and lacked examples. It was then decided to write it again, taking advantage of -some remarks of the students to whom it had been partly addressed. The actual text is this second version. The subject matter is stability theory in the general setting of ordinary differential equations using what is known as Liapunov''s direct or second method. We concentrate our efforts on this method, not because we underrate those which appear more powerful in some circumstances, but because it is important enough, along with its modern developments, to justify the writing of an up-to-date monograph. Also excellent books exist concerning the other methods, as for example R. Bellman [1953] and W. A. Coppel [1965].

In instituting its prospective studies the European Cultural Founda­ tion has to some extent gone against tradition. Until now those who were deeply committed to the idea of a European Community looked into the past rather than into the future for bases on which the com­ munity could be integrated. However, if we want a European society to become a reality it must be built on the basis of shared fundamental values. The majority of publications dealing with a unified or inte­ grated Europe have until now accepted that this foundation guarantee­ ing the stability of a future European society should be found in certain common elements of the history of the European nations. The futurological studies instituted by the European Cultural Foun­ dation have not rejected this mode of approach outright. They have respected the historical framework indispensable to any futurological undertaking. But the research and discussions of the groups working within the framework of Plan Europe 2000 offer increasing support to the conviction expressed by Gaston Deurinck in the first words of his introduction to the present study: "The future does not exist .. thf> future is to be created, and before being created, it must be conceived, it must be invented, and finally willed" ..