Geometrical Dynamics of Complex Systems is a graduate-level monographic
textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical
dynamicsofcomplexsystemsofvariousnatures. By'complexsystems', inthis
book are meant high-dimensional nonlinear systems, which can be (but not
necessarily are) adaptive. This monograph proposes a uni?ed
geometrical - proachtodynamicsofcomplexsystemsofvariouskinds:
engineering, physical, biophysical, psychophysical, sociophysical,
econophysical, etc. As their names suggest, all these multi-input
multi-output (MIMO) systems have something in common: the underlying
physics. However, instead of dealing with the pop- 1 ular 'soft
complexity philosophy', we rather propose a rigorous geometrical and
topological approach. We believe that our rigorous approach has much
greater predictive power than the soft one. We argue that science and
te- nology is all about prediction and control. Observation,
understanding and explanation are important in education at
undergraduate level, but after that it should be all prediction and
control. The main objective of this book is to show that
high-dimensional nonlinear systems and processes of 'real life' can be
modelled and analyzed using rigorous mathematics, which enables their
complete predictability and controllability, as if they were linear
systems. It is well-known that linear systems, which are completely
predictable and controllable by de?nition - live only in Euclidean
spaces (of various - mensions). They are as simple as possible,
mathematically elegant and fully elaborated from either scienti?c or
engineering side. However, in nature, no- ing is linear. In reality,
everything has a certain degree of nonlinearity, which means:
unpredictability, with subsequent uncontrollability.