Moreira, Carlos Gustavo; Yoccoz, Jean-Christophe Stable intersections of regular Cantor sets with large Hausdorff dimensions. (English) Zbl 1195.37015 Ann. Math. (2) 154, No. 1, 45-96 (2001); corrigendum ibid. 154, No. 2, 527 (2001); erratum ibid. 195, No. 1, 363-374 (2022). Summary: We prove a conjecture by J. Palis [Differential equations, Proc. Lefschetz Centen. Conf., Mexico City/Mex. 1984, Pt. III, Contemp. Math. 58.3, 203–216 (1987; Zbl 0617.58027)] according to which the arithmetic difference of generic pairs of regular Cantor sets on the line either has zero Lebesgue measure or contains an interval. More precisely, we prove that if the sum of the Hausdorff dimensions of two regular Cantor sets is bigger than one then, in almost all cases, there are translations of them whose intersection persistently has Hausdorff dimension. Cited in 4 ReviewsCited in 60 Documents MSC: 37C45 Dimension theory of smooth dynamical systems 28A78 Hausdorff and packing measures 28A80 Fractals 37D05 Dynamical systems with hyperbolic orbits and sets 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37G25 Bifurcations connected with nontransversal intersection in dynamical systems Citations:Zbl 0617.58027 PDF BibTeX XML Cite \textit{C. G. Moreira} and \textit{J.-C. Yoccoz}, Ann. Math. (2) 154, No. 1, 45--96 (2001; Zbl 1195.37015) Full Text: DOI OpenURL