Catastrophe, Chaos, Synergetics and Thermodynamics. A Unified Approach via Information of Deterministic Maps
Shannon information theory contains in itself all the elements which we need to define the entropy of deterministic patterns; without using probability, but in a way which is nevertheless fully consistent with its framework. Shannon entropy, Renyi entropy and entropies of family of deterministic maps are so obtained. We can then define thermodynamic entropy of deterministic maps, therefore the thermodynamic meaning of the Liapunov exponent so useful in the analysis of chaotic dynamics. The relation between the se entropies of maps and synergetics is exhibited, and one examines the types of results one may so expect when applies the model to the catastrophe theory.
KeywordsShannon Entropy Catastrophe Theory Renyi Entropy Thermodynamic Entropy Liapunov Exponent
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