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Title: Dynamical Systems and Chaos: A Mathematical Perspective
Abstract: A Dynamical System is a set of ordinary differential (or difference) equations, in continuous (or discrete) time and space. These equations are generally non-linear and very difficult to solve analytically. When they are solved numerically, they are often found to exhibit unpredictable, or as we say “chaotic” behavior (or “chaos”). A first fundamental question, therefore, is whether there are parameter values, for which these equations are analytically solvable.
In this lecture, we will show that these cases are very rare. What is most common is that solutions are generally “chaotic”, in other words, they exhibit an “extremely sensitive dependence on the initial conditions”, which we call “chaos”. We will then study in detail some examples of dynamical systems, which help us better understand the concepts of “predictability” and “chaos”, using examples of dynamical systems, which are often encountered in applications to physics, chemistry, biology, and also engineering science.
Prof Bountis Anastasios (Tassos)
Speaker
Prof Dr Bountis Anastasios (Tassos)
Professor Emeritus of Mathematics
Department of Mathematics
Center of Research & Applications of Non-Linear Systems
University of Patras
Anastasios (Tassos) Bountis is Professor Emeritus of the Department of Mathematics, University of Patras, Greece, where he was Professor from 1990 to 2016, and director of the Center for Research and Application of Nonlinear Systems. In 2014 he was elected Corresponding Member of the Academy of Athens in the chair of complex systems.
In 2015 he was elected member of the European Academy of Science and Arts, at Salzburg. In 2024, he was awarded the G.M. Zaslavsky Award for outstanding scholars in Nonlinear Physical Science. He obtained his Ph.D. degree in Physics from the University of Rochester, N.Y., in 1978, and has taught at universities in the U.S.A. until 1985.
He was invited lecturer and researcher in several countries in Europe, Mexico, India, Japan, Brazil, New Zealand, Australia and South Korea. His research has been supported by many U.S., European and Greek grants, including an ORAU grant from Nazarbayev University and a grant of the Russian Ministry of Education. He has organized in Greece 5 international conferences, 30 Greek summer schools and 5 PhD Schools on “Nonlinear Dynamics and Complexity”.
He has authored 7 books in Greek and one in English on “Complex Hamiltonian Dynamics” (Springer Synergetics, 2012). He has supervised 20 M.Sc. theses and 15 Ph.D. theses and is on the Editorial Board of 5 International Journals. He has published more than 170 papers in refereed journals, 58 in conference proceedings, and has nearly 7300 citations, h-index: 45, i10-index:141 (Google Scholar). https://thalis.math.upatras.gr/~bountis/
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