Abstract
For the Hénon mapT a, b(x, y) = (1 −ax 2 +y, bx), Benedicks and Carleson proved that for (a,b) near (2, 0) andb > 0, there exists a setE with positive Lebesgue measure, whose corresponding mapT a, b possesses a strange attractor. Viana conjectured that if (a, b) ∈E, then the nonwandering set of the mapT a, b Ω(Ta, b) = ∧a, b,Uq a, b, where ∧a, b, is the strange attractor, qa,b is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E1 ⊂E.
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Cao, Y. The nonwandering set of some Hénon map. Chin. Sci. Bull. 44, 590–594 (1999). https://doi.org/10.1007/BF03182714
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DOI: https://doi.org/10.1007/BF03182714