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Abundance of non-uniformly hyperbolic Hé...
Berger, Pierre...

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Abundance of non-uniformly hyperbolic Hénon like endomorphisms by Berger, Pierre ( Author )
Lemonjar Open Access
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09-03-2009
For every C2-small function B, we prove that the map (x,y)↦(x2+a,0)+B(x,y,a) leaves invariant a physical, SRB probability measure, for a set of parameters a of positive Lebesgue measure. When the perturbation B is zero, this is the Jakobson Theorem; when the perturbation is a small constant times (0,x), this is the celebrated Benedicks-Carleson Theorem. In particular, a new proof of the last theorem is given, based on devellopment of the combinatorial formalism of the Yoccoz puzzles. By adding new geometrical and combinatorial ingredients, and restructuring classic analytical ideas, we are able to carry out our proof in the C2-topology, even when the underlying dynamics are given by endomorphisms.
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English
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MYR 0.00
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http://arxiv.org/abs/0903.1473
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