In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjects of science, such as mathematical topology, relativity or particle physics. For this reason, the tools of NLTS have been confined and utilized mostly in the fields of mathematics and physics. However, many natural phenomena investigated I many fields have been revealing deterministic non linear structures. In this book we aim at presenting the theory and the empirical of NLTS to a broader audience, to make this very powerful area of science available to many scientific areas. This book targets students and professionals in physics, engineering, biology, agriculture, economy and social sciences as a textbook in Nonlinear Time Series Analysis (NLTS) using the R computer language.
On Rational Knots and Links in the Solid Torus
