48 citations · 272 across the 33 of their papers we have counts for
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On multifractal formalism for self-similar measures with overlaps
Julien Barral, De-Jun Feng
Let be a self-similar measure generated by an IFS of similarities on (). When is dimensional regular (see Definition~1.1), we g…
Dimensions of random statistically self-affine Sierpinski sponges in
Julien Barral, De-Jun Feng
We compute the Hausdorff dimension of any random statistically self-affine Sierpinski sponge () obtained by using some percolation process in $[0,1]…
Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet
Julien Barral, De-Jun Feng
In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjectur…
Localized asymptotic behavior for almost additive potentials
Julien Barral, Yan-Hui Qu
We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost additive continuous potentials on a topologically mixing subshift o…
Multifractal analysis and localized asymptotic behavior for almost additive potentials
Julien Barral, Yan-Hui Qu
We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost-additive continuous potentials on a topologically mixing subshift o…
Weighted thermodynamic formalism and applications
Julien Barral, De-Jun Feng
Let and be two subshifts so that is a factor of . For any asymptotically sub-additive potential on and $\ba=(a,b)\in\R^2$ with , , we i…