A Quantitative Bifurcation Analysis of Hénon-Like 2D Maps

Details A Quantitative Bifurcation Analysis of Hénon-Like 2D Maps A Quantitative Bifurcation Analysis of Hénon-Like 2D Maps

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..66..365p&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 66, Issue 4, pp.365-385

Astronomy and Astrophysics

Astronomy

3

Bifurcations, Maps

Scientific paper

We numerically study the bifurcations of two nonlinear maps, with the same linear part, which depend on a parameter namely the Hénon quadratic map and the so called ‘beam-beam’ map. Many families of periodic orbits which bifurcate from the central family, are studied. Each family undergoes a sequence of period doubling bifurcations in the quadratic map, But the behavior of the ‘beam-beam’ map is completely different. Inverse bifurcations occur in both maps. But some families of the same type which bifurcate inversely in the quadratic map do not bifurcate inversely in the ‘beam-beam’ map, even though both maps have common linear part.

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