Dimension maximizing measures for self-affine systems
Bal\'azs B\'ar\'any, Micha{\l} Rams
TL;DR
This paper investigates the dimension theory of planar self-affine sets with dominated splitting and strong separation, establishing the existence of Gibbs measures that maximize dimension and analyzing their properties.
Contribution
It proves the existence of dimension maximizing Gibbs measures for certain self-affine systems and extends the Ledrappier-Young formula to these measures.
Findings
Existence of dimension maximizing Gibbs measures (Käenmaki measures).
Ledrappier-Young formula holds for Gibbs measures.
Introduces a transversality condition for strong-stable directions.
Abstract
In this paper we study the dimension theory of planar self-affine sets satisfying dominated splitting in the linear parts and strong separation condition. The main results of this paper is the existence of dimension maximizing Gibbs measures (K\"aenm\"aki measures). To prove this phenomena, we show that the Ledrappier-Young formula holds for Gibbs measures and we introduce a transversality type condition for the strong-stable directions on the projective space.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.