<p>Synthesis report on the programme</p><p>Stability and Instability in Mechanical Systems, proposed by Amadeeu Delshams, Raphael de la Llave, and Tere M. Seara</p><p>The following is a compiled version of the concurrent positive evaluations.</p><p>The research programme is planned in the fall of 2008, with expected starting date 1st of September and ending date 31st of December. The proposal is well structured and carefully planned. </p><p>The topic is related to classical questions concerning stability, and is currently a fast developing area of research with different methods applied. The topics are relevant in theoretical mathematics, scientific computing and applications in astrophysics and chemistry. It links rigorous mathematics with more experimental methods. The goal is to analyze the state of the art, and to compare and unify the different methods. </p><p>The list of leading researchers in the field who have already accepted to participate is absolutely impressive. It would be valuable to have - as soon as possible - a more detailed plan for who would be visiting when.</p><p>An external scientific committee is proposed. It should oversee all the activities and generate activities. It consists of the three organizers and four others, who have all accepted. All are of very high scientific standard. This makes a truly international committee, with three local researchers from the Barcelona area and four from outside Spain. </p><p>The planned activities consists of two workshops, each to be preceded by an advanced course, and weekly working seminars, which will be coordinated with other activities in dynamical systems in the Barcelona area. (The dates of the second workshop and the advanced course seem to have been interchanged in the writing.) The activities are embedded in a series of conferences and workshops, which have already happened internationally or will take place in the near future. This is well documented. Hence, we can be pretty sure that the organizers have checked that there is no other related activity that overlaps with the programme. The two workshops have different focuses: the first on Recent progress and mathematical theory, and the second on Applications and numerical tools. Moreover, as an important outcome of the semester, the proposal includes the objective of turning the series of lectures for graduate students into a book to cover the modern developments within the area. It has been agreed with some universities in the Barcelona area that the courses will receive credit as graduate courses. – It would be valuable to specify the credit in terms of the ECTS.</p><p>The application is based on very strong groups of specialists in the Barcelona area. Moreover, the three organisers have been co-authors of a recent monograph, which deals with the recent progress of the theory. They have contributed strongly to the study of infinite dimensional dynamical systems.</p><p>The proposal is judged to be excellent with a high expected impact, both locally and internationally. </p>