Numerical Study Of Coexisting Attractors For The Henon Map

• The question of coexisting attractors for the Henon map is studied numerically by performing an exhaustive search in the parameter space. As a result, several parameter values for which more than two attractors coexist are found. Using tools from interval analysis, we show rigorously that the attractors exist. In the case of periodic orbits, we verify that they are stable, and thus proper sinks. Regions of existence in parameter space of the found sinks are located using a continuation method; the basins of attraction are found numerically.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Henon map

periodic orbit

coexisting attractors

interval arithmetic

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