Stable intersections of conformal cantor sets.
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2021
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We investigate stable intersections of conformal Cantor sets and their consequences to
dynamical systems. First we define this type of Cantor set and relate it to horseshoes appearing in automor-
phisms of C2
. Then we study limit geometries, objects related to the asymptotic shape of the Cantor sets,
to obtain a criterion that guarantees stable intersection between some configurations. Finally we show that
the Buzzard construction of a Newhouse region on Aut(C2
) can be seem as a case of stable intersection of
Cantor sets in our sense and give some (not optimal) estimative on how “thick” those sets have to be.
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ARAÚJO, H.; MOREIRA, C. G. Stable intersections of conformal cantor sets. Ergodic Theory and Dynamical Systems, 2021. Disponível em: <https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/abs/stable-intersections-of-conformal-cantor-sets/2E06382177A6A08D776BBC27FB2B0445#>. Acesso em: 29 abr. 2022.