Deflation techniques for the determination of periodic solutions of a certain period

Details Deflation techniques for the determination of periodic solutions of a certain period Deflation techniques for the determination of periodic solutions of a certain period

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003ap%26ss.288..591k&link_type=abstract

Astrophysics and Space Science, v. 288, Issue 4, p. 591-599 (2003).

Astronomy and Astrophysics

Astrophysics

Scientific paper

The computation of periodic orbits of nonlinear mappings or dynamical systems can be achieved by applying a root-finding method. To determine a periodic solution, an initial guess should be located within a proper area of the mapping or a surface of section of the phase space of the dynamical system. In the case of Newton or Newton-like methods these areas are the basins of convergence corresponding to the considered solution. When several solutions of the same period exist in a particular region, then the deflation technique is suitable for the calculation of all these solutions. This technique is applied here to the Hénon's mapping and the driven conservative Duffing's oscillator.

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