Abstract
We study the destruction of hyperbolic sets (horseshoes) in parametrizedfamilies of diffeomorphisms through homoclinic tangencies taking placeinside the limit set. If the limit set at the tangency parameter has smalldimension (limit capacity) then hyperbolicity prevails after thebifurcation (full Lebesgue density). We also prove that, if that limit set isthick then the system exhibits homoclinic tangencies for a wholeparameter interval across the bifurcation. These results are based on ageometric analysis of the limit set at the tangency, including a statementof bounded distortion.
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