Chaotic dynamical systems: on de-chaotification of dynamical systems and on augmenting the generalized Lorenz normal form
Abstract
Chaotic dynamical systems comprise an actively developed research field spanning quite a number of different scientific disciplines. It is only in the last few decades that we perceive a unification of techniques theoretical and experimental treatments (regarding data acquisition numerical computations and algorithms programming) resulting in sometimes spectacular amalgamations of hitherto seemingly disjoint areas of research effectively giving birth to what we call today Chaos Theory. The subject of this Dissertation is to provide insight into the study of certain classes of dynamical systems to state some of their characteristic properties following in principle standard methodology focusing on the particular properties that those systems possess. We present a new method of characterization of the qualitative behavior of systems modeled as discrete mappings and a new broader class of three dimensional continuous time dynamical systems modeled as systems of ordinary differential equat ...
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