The Multiplicative Golden Mean Shift Has Infinite Hausdorff Measure

Hausdorff dimension of the multiplicative golden mean shift

On the Spectrum of Infinite Dimensional Random Products of Compact Operators

We consider an infinite dimensional separable Hilbert space and its family of compact integrable cocycles over a dynamical system f . Assuming that f acts in a compact Hausdorff space X and preserves a Borel regular ergodic measure which is positive on non-empty open sets, we conclude that there is a residual subset of cocycles within which, for almost every x, either the OseledetsRuelle’s deco...

2 4 D ec 1 99 8 Hausdorff dimension , Mean quadratic variation of infinite self - similar measures ∗

Under weaker condition than that of Riedi & Mandelbrot, the Hausdorff (and Hausdorff-Besicovitch) dimension of infinite self-similar set K ⊂ R which is the invariant compact set of infinite contractive similarities {Sj(x) = ρjRjx + bj}j∈N (0 < ρj < 1, bj ∈ R , Rj orthogonal) satisfying open set condition is obtained. It is proved (under some additional hypotheses) that the β-mean quadratic vari...

Application of measures of noncompactness to infinite system of linear equations in sequence spaces

G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.  

An Extension of Hawkes' Theorem on the Hausdorff Dimension of a Galton-watson Tree

Let T be the genealogical tree of a supercritical multitype Galton–Watson process, and let 3 be the limit set of T, i.e., the set of all infinite self-avoiding paths (called ends) throughT that begin at a vertex of the first generation. The limit set3 is endowed with the metric d(ζ, ξ) = 2−n where n = n(ζ, ξ) is the index of the first generation where ζ and ξ differ. To each end ζ is associated...