Volume 11, Number 2, 2008

EDITORIAL

This volume contains papers selected from manuscripts submitted to the Editorial Committee by participants of the 20^th Summer School - Conference on "Nonlinear Science and Complexity", which took place at the Conference Center of the University of Patras, 19 - 29 July, 2007. As in all previous such events, the aim of the Organizing Committee was to bring together distinguished teachers and researchers working in various fields of Nonlinear Science and Complexity to give introductory lectures and present their recent results on a topic of their specialty. As in all other cases in the past, many Greek as well as European scientists accepted our invitation and participated in this event, contributing also their manuscripts for publication in a volume containing the Proceedings of the 20^th meeting of this series.

What was not, however, the same "as in all other such past events" was the absence of one of the founding fathers of these 20 Summer School - Conferences, our beloved friend and colleague Professor Simos Ichtiaroglou, who passed away suddenly one month before the meeting, at his home in Thessaloniki. Simos was only 58 years old and the news shocked the Greek scientific community and many colleagues around the world, who appreciated not only his important contributions to Nonlinear Science, but also his genuinely friendly, human and sincere character that made him so popular among his students and collaborators.

Thus, the 20^th School was very different than all previous ones in this respect: Simos was not with us to ask questions during the lectures, to engage in endless discussions with students in the evenings and to take out his guitar, when all conversations about science were over, and start to play. We, the members of this Editorial Committee, feel it is our duty, before we present the contents of this volume, to give a short account of the work of Simos Ichtiaroglou as a scientist. We will not speak about Simos Ichtiaroglou the man; that would be pointless for those who knew him, while for those who never had the privilege to meet him, we are afraid our words might be too inadequate to accurately describe Simos' personality.

Simos Ichtiaroglou (1950 - 2007) was born in the city of Thessaloniki, in Northern Greece, where he spent most of his life. He obtained his undergraduate degree in Physics from the University of Thessaloniki in 1972, as well as an M. Sc. degree in Electronics in 1978 from the same university. He then turned his attention to the fields of Celestial Mechanics and Astronomy that excited him the most and went on to obtain his Ph.D. degree from the Department of Physics of the University of Thessaloniki in 1982, working under the supervision of Professor John Hadjidemetriou. He became a Lecturer in 1982 and an Assistant Professor of the Department of Physics at the same University in 1984 and started to develop his scientific activities in several fields in Dynamics and Theoretical Mechanics.

Simos was instrumental in the organization of the first international Conference on "Nonlinear Dynamics and Chaos" in Greece, which took place at Thessaloniki in the summer of 1986. There, he met several scientists who worked in similar fields as he did but from a more mathematical and rigorous perspective. This was a turning point in Simos' career, as it signalled the beginning of his devotion to the study of the mathematical foundations of Hamiltonian dynamical systems, symplectic maps, periodic orbits and their stability and the areas of integrability and non-integrability of Hamiltonian systems, which were to occupy, from then on, most of his scientific efforts. In 1991 he was elected Associate Professor at the University of Thessaloniki, a position in which he became distinguished not only for his research, but also his ability in teaching, writing books and developing courses in Theoretical Mechanics, Nonlinear Dynamics and Dynamical systems and Chaos.

Beyond the above topics, Simos became interested more recently in various other areas of dynamical systems relevant to real - life problems, like breathers in 1-dimensional lattices, dynamics and dislocations in solids, bifurcation theory and applications to population dynamics. He guided the Ph. D. theses of several students, some of whom went on to occupy faculty positions at the same Department to continue Simos' tradition in Nonlinear Science at the University of Thessaloniki. All of us, students and colleagues will miss him, not only for his scientific contributions and clear lectures at our summer schools, but also for his exceptionally warm and friendly personality.

Many of the speakers of our 20^th Summer School - Conference of July, 2007 submitted manuscripts to be included in this volume of Proceedings, as a tribute to the memory of Simos Ichtiaroglou, and we wish to thank the Editors of Nonlinear Phenomena in Complex Systems for agreeing to publish it as a special issue of their journal. Some of the authors were invited speakers from abroad, like Professor C. Jung from the Universidad Autonoma de Mexico, who lectured on molecular vibrations and Professor A. Rauh of the University of Oldenburg, Germany, who talked about hydrodynamics and wind energy technology.

These contributions, as well as those of Greek scientists who knew Simos intimately, like Professor G. Contopoulos and Professor J. Hadjidemetriou are presented in this volume under the title of "Review Papers". We have also included under this heading the very informative articles by Professor D. Ghikas on quantum information and Dr. Y. Kominis on canonical perturbation theory and wave-particle interactions.

In the second part of the issue, we present 21 contributions by Greek and European scientists, with emphasis on recent results in different fields of Nonlinear Science and Complexity. These original articles have been reviewed and are published here under the title "Research Papers". They cover a wide variety of themes like: Astronomy and the spiral structure in disk galaxies, power prices in competitive markets, mutual information and time series analysis, nonlinear differential equations, electrical brain signal integration, localization in metamaterials, trimolecular reactive systems, nonlinear electric circuits, classical and quantum chaos in multiphoton dissociation, etc. We have also included in this section the last paper co - authored by Simos Ichgtiaroglou on large-scale chaos in the problem of homogeneous magnetization.

Nonlinear Science and Complexity have emerged as a new scientific direction of the 21st century, aiming to provide new ideas and methods for solving outstanding complex problems in many scientific fields. They rely on the mathematics of dynamical systems, the theory of chaos and the geometry of fractals, as well as novel techniques of numerical simulations, computational intelligence approaches and experimentation.

We believe that the 20^th Summer School - Conference of Patras, in July, 2007 and its Proceedings presented in this volume have served well the purpose of presenting to a new generation of scientists some of the recent developments of Nonlinear Science and Complexity. Guided by the inspiration of scientists like Simos Ichtiaroglou and a 20 - year tradition of pioneering Greek contributions, we expect that we will be able to continue this series of Summer School - Conference events in the future, making Greece a focal point in the advancement of the study of nonlinear phenomena in complex systems.

March 2008.

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