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non-uniformly hyperbolic horseshoes

Journal of the Institute of Mathematics of Jussieu (1)

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STABLE SETS OF CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE THE EXPECTED DIMENSION
Part of
Carlos Matheus, Jacob Palis, Jean-Christophe Yoccoz
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 1 / January 2021

Published online by Cambridge University Press:

04 April 2019, pp. 305-329

Print publication:

January 2021
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We show that the stable and unstable sets of non-uniformly hyperbolic horseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms have the value conjectured in a previous work by the second and third authors of the present paper. Our results apply to first heteroclinic bifurcations associated with horseshoes with Hausdorff dimension ${<}22/21$ of conservative surface diffeomorphisms.