Work

Dimension of Planar Non-conformal Attractors with Triangular Derivative Matrices

Year: 2024

Type: article

Abstract: We study the dimension of the attractor and quasi-Bernoulli measures of parametrized families of iterated function systems of non-conformal and non-affine maps. We introduce a transversality condition under which, relying on a weak Ledrappier-Young formula, we show that the dimensions equal to the root of the subadditive pressure and the Lyapunov dimension, respectively, for almost every choice of parameters. We also exhibit concrete examples satisfying the transversality condition with respect to the translation parameters.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-024-05131-2

Authors: Balázs Bárány, Antti Käenmäki

Institutions: Budapest University of Technology and Economics, HUN-REN Alfréd Rényi Institute of Mathematics

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funders: Budapesti Műszaki és Gazdaságtudományi Egyetem, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, Nemzeti Kutatási, Fejlesztési és Innovaciós Alap