The nonwandering set of some Hénon map |
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Authors: | Yongluo Cao |
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Institution: | 1. Department of Mathematics, Suzhou University, 215006, Suzhou, China
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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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Keywords: | |
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