Dimension results for inhomogeneous Moran set constructions

Historic set carries full hausdorff dimension

‎We prove that the historic set for ratio‎ ‎of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional‎ ‎non-uniformly hyperbolic dynamical systems.

Stability results for set solution of fuzzy integro-differential systems

Hausdorff dimension and oracle constructions

Bennett and Gill (1981) proved that P 6= NP relative to a random oracle A, or in other words, that the set O[P=NP] = {A | P = NP} has Lebesgue measure 0. In contrast, we show that O[P=NP] has Hausdorff dimension 1. This follows from a much more general theorem: if there is a relativizable and paddable oracle construction for a complexity-theoretic statement Φ, then the set of oracles relative t...

A Multifractal Analysis of Gibbs Measures for Conformal Expanding Maps and Markov Moran Geometric Constructions

We establish the complete multifractal formalism for Gibbs measures for confor-mal expanding maps and Markov Moran geometric constructions. Examples include Markov maps of an interval, hyperbolic Julia sets, and conformal toral endomorphisms. This paper describes the multifractal analysis of measures invariant under dynamical systems. The concept of a multifractal analysis was suggested by seve...

Algebraic constructions on set partitions

The main contribution of this article is to provide a combinatorial Hopf algebra on set partitions, which can be seen as a Hopf subalgebra of the free quasi-symmetric functions, and which is free, cofree and self-dual. This algebraic construction comes naturally from a combinatorial algorithm, an analogous of the Robinson-Schensted correspondence on set partitions. This correspondence also give...