CAMTP home 8th International Summer School/Conference
Center for Applied Mathematics and Theoretical Physics
CAMTP, University of Maribor, Slovenia
26 June - 10 July 2011


Chaos, either classical or quantum, conservative or dissipative, pure or applied, has become a fashionable subject of pronounced activities of nonlinear science during the recent decades. It is attracting the attention of not merely scientists in the relevant and related multidisciplinary and interdisciplinary scientific fields but even of philosophers or writers, coming up in daily papers and popular magazines. It often gives rise to turbulent controversies and disputes concerning its scientific merit and its practical use. Today, this field of research is very well established, it is immensely important in both pure science and in technology, and in fact might be considered as one of the scientific revolutions of 20th Century, extending its fast development into the 21st Century. It has a great and very important future for many centuries to come. In broader sense, it simply encompasses the totality of complex systems in nature, technology and society.

In August 1992, a group of students at the University of Ljubljana, led by the initiator Mrs. Maja Malus, came up with the idea to organize a summer school covering the variety of topics in pure and applied research on chaos. The main organizational effort was undertaken by the voluntary student staff under the direction of Maja Malus, then undergraduate student of electrical engineering at the University of Ljubljana and with active support of the international student association IAESTE. The scientific advisory board of the School (Professors Igor Grabec, Marko Robnik and Aneta Stefanovska) set up in March 1993, enjoyed the enthusiasm of the students, their devotion and hard work which eventually resulted in a very successful meeting. Financial support of many Slovenian sponsoring and donating companies and institutions, especially IBM Slovenia and the Ministry of Science and Technology, was highly appreciated and acknowledged. The hard and enthusiastic work of the student staff, the technical organizer of the School, was crowned with the prestigious charter and the golden tablet of the University of Ljubljana, for the "...exceptional achievements in organizing the International Summer School...".

The Summer School has become a tradition now: The second School was held at the University of Ljubljana in August 1994 (one week), and the third one on 24 June - 5 July 1996 at the University of Maribor, as a part of the activities of CAMTP. The 4th School/Conference held at CAMTP, University of Maribor, on 27 June - 11 July 1999 was again very successful indeed, for we had 37 invited lecturers from all over the world, from all continents, and in total about 105 participants. The fifth School/Conference, held traditionally at CAMTP on 30 June - 14 July 2002, was even stronger, as we had 40 invited lecturers and speakers from all over the World, and altogether about 130 participants. In 2005 we had 46 invited lecturers and 68 other participants, and in 2011 again 46 invited lecturers and 38 other participants. All Schools were strongly international, in the sense that about 90% of all participants (lecturers and "students") were from abroad. The lecturers, about twelve in 1993 and 1994, and about 27 in 1996, 37 in 1999, 40 in 2002, 46 in 2005 and again in 2088 were from among the leading scientists in the relevant scientific disciplines, from many countries worldwide, including USA, Canada, Russia, Japan, Western Europe, Israel, etc. The School was intellectually dignified by the attendance and the lectures of such distinguished scientific scholars as Professor Boris Chirikov from Novosibirsk, Russia, Professor Siegfried Großmann from Marburg, Germany, Professor Giulio Casati from Como, Italy, Professor Erik Mosekilde from Lyngby, Denmark, Professor Uzy Smilansky from Rehovot, Israel, Professor Hermann Haken from Stuttgart, Germany, Professor Predrag Cvitanović from Atlanta, USA, Professor Oriol Bohigas from Orsay, France, Professor Giovanni Gallavotti from Rome, Italy, Professor George Contopoulos from Athens, Greece, Professor Yoshiki Kuramoto, Kyoto, Japan, Professor Yoji Aizawa from Tokyo, Japan, Professor Tassos Bountis from Patras, Greece, Professor Theo Geisel from Göttingen, Germany, Professor Pierre Gaspard from Brussels, Belgium, Professor Hans A. Weidenmüller from Heidelberg, Germany, and many others.

It should be mentioned that since 2002 we have the tradition that the Summer School & Conference is dedicated to some prominent physicists, namely: Hermann Haken in 2002 on occasion of his 75th birthday, Siegfried Grossmann in 2005 on occasion of his 75th birthday, and Giulio Casati in 2011 on occasion of his 65th birthday. This year, in 2011, it is dedicated to Professor Predrag Cvitanović on occasion of his 65th birthday. More about that please see on page 11.

Therefore our 8th International Summer School/Conference "Let's Face Chaos through Nonlinear Dynamics" is a natural continuation of this tradition, again in the same environment as in 2011, 2005, 2002, 1999 and 1996, namely at the University of Maribor, as one of the activities carried out by CAMTP, in the period 26 June through 10 July 2011. This environment proved indeed to be ideal for such purposes for many reasons, including the rich cultural life offered by the marvelous performances on the world top level of the Maribor Festival Lent, the sportific facilities, the mountains and hiking there, the excellent local Slovenian wines and wine tasting tour, the touristic attractions, our excellent private concerts performed by our young Slovenian musicians, exhibitions of fine arts, excursions through Slovenia, fireworks that accompany the closing of the Festival Lent, etc. This time we shall again enjoy some very interesting public evening lectures. One of them will be delivered by Professor Mrs. Sara A. Solla of Northwestern University, Evanston, USA, on Monday 4 July 2011 at 21:00, about the neurosciences.

The scientific programme is covering the broad interdisciplinary and multidisciplinary field of nonlinear dynamics and synergetics, concerning applications and manifestations of chaos in diverse fields of human knowledge, ranging from mathematics to physics and chemistry, from medicine to economy, from biology to engineering, and includes even sociological aspects. It seems natural for us to speak about chaos versus order in an interdisciplinary context. The organizers of this School/Conference share the belief that interdisciplinary trends and developments in science are of primary importance, especially in order to counteract the strongly increasing specialization taking place in the science and technology in our most modern era, however certainly not at the expense of the quality of the disciplinary research: In order to achieve strong interdisciplinarity we certainly need in the first place strong disciplinarity. There is an obvious and urgent need for meetings of this kind, giving an opportunity of scientific exchange among seemingly distant disciplines, and, most of all, allowing students and junior scientists to better understand the role of interdisciplinary research, and to bring them in touch with science in making. And to offer them the opportunity to present their own research work (in short reports and posters). To promote most talented young people from all over the world.

It should be emphasized that the physics of complex systems, nonlinear dynamics and synergetics are surely one of the major branches of science and research in the 21st Century, along with elementary particles, astrophysics, biophysics, molecular biology, genetics, medicine, economy, psychology, sociology, new technologies like nanotechnologies, almost all of which are in fact also to some considerable extent the area where the nonlinear dynamics is applicable in an important way. As such the nonlinear dynamics paves the way of future science and technology of complex systems in the 21st Century.

The level at the beginning of each lecture course (delivered by invited lecturers as a series of one-hour (60 minutes) lectures) will be adapted to the advanced undergraduate students (3rd and 4th year) and graduate students (most of the students usually are Ph.D. students (research students) and junior postdocs), but there are also many senior postdocs, junior scientists/professors and senior scientists/professors, whilst in closing the series of lectures (the last third or so) may be and typically will be at the conference level, containing the most recent results comprehensible for the majority of the audience and subject to the discussion among the attending invited speakers, experts and specialists.

The structure of the School & Conference this year will be slightly changed as follows.

In the first week we shall have mainly school programme consisting of five 5-hours lecture courses (each hour 60 minutes):

  1. Predrag Cvitanović, Atlanta, USA: Fluid dynamics and turbulence

  2. Thomas Guhr, Duisburg-Essen, Germany: Econophysics

  3. Tomaž Prosen, Ljubljana, Slovenia:Nonequilibrium classical and quantum statistical mechanics

  4. Aneta Stefanovska, Lancaster, England: Nonlinear dynamics of life: nonautonomous systems, biological oscillators, cellular, cardiovascular and brain dynamics and interactions

  5. Hans-Jürgen Stöckmann, Marburg, Germany: Quantum chaos and random matrix theories

Nevertheless, there will be also some conference presentations and/or short two-hours lecture courses.

In the second week we shall have mainly the conference programme, but nevertheless the lectures will still be at the colloquium level, thus including a good introduction for the nonspecialists and general physics audience. There might be also a few additional mini lecture courses (2 hours each).

The session for short reports (contributed talks) presented by the participants will be mainly on Saturday 2 July 2011 in the morning until lunch time. The posters will be on display during the entire period of the School/Conference, that is two weeks.

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