Intersections of Cantor Sets and Transversality of Semigroups

By H. Furstenberg. 2015

128 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/32613dd101b54370b0094aa17dd5135638f5422b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

Citations in the corpus

A proof of Furstenberg's conjecture on the intersections of ⨯p- and ⨯q-invariant sets (2016, methodology): “In the rest of this section, we will follow Furstenberg [15] to construct an ergodic CPdistribution (with dimension γ) on the space of measures which are supported on slices of K with slopes in [1, 1/β].”
Equidistribution from fractal measures (2013, methodology): “An important phenomenon concerning these maps is measure rigidity: a well-known conjecture of Furstenberg states that, if m 6∼ n, then the only probability measures jointly invariant under Tm and Tn are combinations of Lebesgue measure and atomic measures on rational points.”
On self-similar sets with overlaps and inverse theorems for entropy (2012, methodology): “F in a zero dimensional set, and this, in turn, is an analog of similar conjectures arising in metric number theory and layed out in [10].”
On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane (2021, background): “Furstenberg [10] on intersections of Cantor sets defined in terms of expansions to bases 2, 3 (the conjecture that motivated this connection has since been resolved by the second author [27] and, independently, by M.”
On Furstenberg's intersection conjecture, self-similar measures, and the Lq norms of convolutions (2016, methodology): “Although in different language, this decomposition of µx can be traced back to Furstenberg [20], and was also used more explicitly in [35] to study the L2 dimensions of µx.”
Assouad Dimension and Fractal Geometry (2020, background): “The first is a beautiful fact, which was first explicitly stated by Käenmäki, Ojala and Rossi [154], but has origins in the work of Furstenberg [114, 115, 116] and Bishop and Peres [34].”