No Access

LIE SERIES TECHNIQUE, LIMIT CYCLE SYSTEMS AND DYNAMICAL INTEGRATION

WILLI-HANS STEEB

International School for Scientific Computing, Rand Afrikaans University, Auckland Park 2006, South Africa

https://doi.org/10.1142/S0129183104006595Cited by:1 (Source: Crossref)

Abstract

The Lie series technique is applied to solve a class of nonlinear differential equations. We show that it includes also the dynamical integration technique. In particular systems with limit cycle behavior are studied. Differential equations with chaotic behavior are also considered with this technique.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

W. Gröbner and H. Knapp, Contributions to the method of Lie series, BI Hochschulskripten, Bibliographisches Institut, Mannheim (1967) . Google Scholar
W.-H. Steeb , The Nonlinear Workbook: Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithms, Gene Expression Programming, Wavelets, Fuzzy Logic with C++, Java and Symbolic C++ Programs , 2nd edn. ( World Scientific , Singapore , 2002 ) . Link, Google Scholar
R. Brown and L. O. Chua, Int. J. Bifur. Chaos 3, 217 (1993). Link, Web of Science, Google Scholar
H. Yoshida, Phys. Lett. A 150, 262 (1990). Crossref, Web of Science, ADS, Google Scholar
U. Parlitz and W. Lauterborn, Phys. Rev. A 36, 1428 (1987). Crossref, Web of Science, ADS, Google Scholar
W.-H. Steeb , Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra ( World Scientific , Singapore , 1996 ) . Link, Google Scholar
H. Hochstadt and B. H. Stephan, Arch. Rat. Mech. Anal. 23, 368 (1977). Google Scholar
R. N. D'Heedene, J. Diff. Eq. 5, 564 (1969). Crossref, Web of Science, ADS, Google Scholar
W.-H. Steeb and A. Kunick, Int. J. Non-Linear Mechanics 17, 41 (1982). Crossref, Web of Science, ADS, Google Scholar