Continuous and discontinuous piecewise-smooth one-dimensional maps : invariant sets and bifurcation structures /
Viktor Avrutin (University of Stuttgart), Laura Gardini (University of Urbino), Irina Sushko (National Academy of Sciences of The Ukraine), Fabio Tramontana (University of Urbino).
Bok Engelsk 2019
| Omfang | xiii, 634 pages : : illustrations (black and white) ;
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| Opplysninger | Publisher's no.: 8258 hc.. - General concepts and tools -- Bifurcations in piecewise smooth maps -- Bifurcation scenarios (overview) -- Map replacement -- Skew tent map -- Adding structures -- Incrementing structures -- Organizing centers.. - "Although the dynamic behavior of piecewise-smooth systems is still far from being understood completely, some significant results in this field have been achieved in the last twenty years. The investigation of these systems is important not only because they represent adequate models for many applications ranging from mechanical and electrical engineering up to financial markets, but also due to the importance of the phenomena observed in other types of dynamical systems as well. It is natural, therefore, to begin the analysis with the most simple subclass of piecewise-smooth systems (namely one-dimensional maps) for which many phenomena can be investigated much more easily than for higher-dimensional systems. In this book, we consider both continuous and discontinuous one-dimensional piecewise-linear maps and summarize the results related to bifurcation structures in regular and robust chaotic domains. The map replacement technique based on symbolic dynamics allows us to offer significantly more analytical proofs than what is usually possible"--
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| Emner | |
| Dewey | |
| ISBN | 9789814368827. - 9814368822
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