Rotation numbers of periodic orbits in the Hénon map

Details Rotation numbers of periodic orbits in the Hénon map Rotation numbers of periodic orbits in the Hénon map

Mar 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988cmaph.120..105a&link_type=abstract

Communications in Mathematical Physics, Volume 120, Issue 1, pp.105-119

Mathematics

Mathematical Physics

6

Scientific paper

For invertible, area-contracting maps of the plane, it is common for a basin of attraction to have a fractal basin boundary. Certain periodic orbits on the basin boundary are distinguished by being accessible (by a path) from the interior of the basin. A numerical study is made of the accessible periodic orbits for the Hénon family of maps. Theoretical results on rotary homoclinic tangencies are given, which describe the appearance of the accessible saddles, and organize them in a natural way according to the continued fractions expansions of their rotation numbers.

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