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Notes on the local analysis of dynamical systems

Confusion is a word we have invented for an order which is not understood.
Henry Miller (1891-1980)

Several terms and definitions related to the local analysis of dynamical systems are presented. Multiple terms for one and the same concept that were found in literature are put together to provide a ``dictionary'' of terms and to avoid potential confusion due to misleading definitions. Additionally, some important concepts which are necessary to analyze a dynamical system are briefly discussed and a new procedure to locally analyze a dynamical system's behavior near trajectory points is proposed. This chapter should give computer graphics specialists, who work on the visualization of analytically defined dynamical systems - but are not experts on the field of dynamical systems - a set of mathematical tools for a thorough investigation of the local behavior of such systems.



 



Helwig Löffelmann, November 1998,
mailto:helwig@cg.tuwien.ac.at.