Friday, September 15,
2017, 3pm
Location: Planetary Hall Room 126
Miguel A. F. SanJuán
Universidad Rey Juan Carlos
Department of Physics
Nonlinear
Dynamics, Chaos, and Complex Systems: A Historical Perspective
Abstract
When we talk about dynamics, we do not only understand
the motion of celestial bodies and solid mechanical systems, but any
changes
with respect to time of one or more variables. From that point of view,
we can
find dynamics everywhere, in any field of science. Thus, now we have a
more
general vision, including stock market movements and economic
variables,
concentration changes in chemical reactions, changes in physiological,
biological and medical variables, action potentials of neurons, etc ...
providing a more interdisciplinary perspective.
The
various interactions between the constituent parts
of a physical system and their feedback mechanisms, are a source of
nonlinearity and complexity, which added to the sensitivity dependence
to
initial conditions which is a hallmark of chaotic behavior, constitutes
a
change of perspective in dynamical systems with important consequences
for the
understanding of science.
I
will give a historical perspective of Nonlinear
Dynamics, Chaos Theory and Complex Systems, including some of the
different
sources that have contributed to the construction of the discipline as
we know
it today. Among them, the three-body problem in celestial mechanics,
turbulence
in fluid dynamics, irreversibility and fundamentals of statistical
physics and
the logistic map and population dynamics in biology. Many schools of
mathematics and physics have played an essential role in the historical
development of the subject, including the French, Russian, Japanese and
American school. The knowledge of this historical perspective allows us
to
understand the breadth of the discipline itself and the multiple
interdisciplinary applications to various fields of science.