We investigate the geodesic motion in D-dimensional Majumdar-Papapetrou multiblack hole spacetimes and find that the qualitative features of the D = 4 case are shared by the higher dimensional configurations. The motion of timelike and null particles is chaotic, the phase space being divided into basins of attraction which are separated by a fractal boundary, with a fractal dimension d B . The mapping of the geodesic trajectories on a screen placed in the asymptotic region is also investigated. We find that the fractal properties of the phase space induces a fractal structure on the holographic screen, with a fractal dimension d B − 1.

Abst ract . T his paper present s t he result s of mult ifract al t est ing of two set s of financial dat a: daily dat a of t he Dow J ones Indust rial Average (DJ IA) index and minut ely dat a of t he Euro St oxx 50 index. W here mult ifract al scaling is found, t he spect rum of scaling exponent s is calculat ed via Mult ifract al Det rended F luct uat ion Analysis. In bot h cases, furt her invest igat ions reveal t hat t he t emporal correlat ions in t he dat a are a more significant source of t he mult ifract al scaling t han are t he dist ribut ions of t he ret urns. It is also shown t hat t he ext reme event s which make up t he heavy t ails of t he dist ribut ion of t he Euro St oxx 50 log ret urns dist ort t he scaling in t he dat a set . T he most ext reme event s are inimical t o t he scaling regime. T his result is in cont rast t o previous findings t hat ext reme event s cont ribut e t o mult ifract ality. Int roduct ionMult ifract al analysis has proved t o be a valuable met hod of capt uring t he underlying scaling st ruct ure present in many types of syst ems via generalised dimensions [1] and f (α) spect ra [2]. T hese syst ems include diff usion limit ed aggregat ion [3][4][5], fluid flow t hrough random porous media [6], at omic spect ra of rare-eart h element s [7], clust erclust er aggregat ion [8] and t urbulent flow [9]. In physiology, mult ifract al st ruct ures have been found in heart rat e variability [10] and brain dynamics [11], and mult ifract al analysis has been helpful in dist inguishing between healthy and pathological patients [12]. Mult ifract al measures have also been found in man-made phenomena such as t he Int ernet [13], art [14] and the stock market [15][16][17].T he concept of mult ifract ality was first int roduced in t he cont ext of t urbulence. It was soon applied t o finance because of it s heavy t ails and long-t erm dependence. T hese two feat ures are also argued t o be present in financial dat a [18,19]. P erforming mult ifract al analysis helps t o increase our knowledge about t he financial syst em and furt her charact erise it . Many st udies have found mult ifract al scaling in financial dat a [20][21][22][23]. An underst anding of t his mult ifract al st ruct ure can enable deeper underst anding of t he dynamics of financial market s. If it is found t o be a universal feat ure of financial dat a, it provides an addit ional benchmark by which t o measure t he fitness of financial models. This in turn can help in the design of well performing port folios and in risk management [17]. a e-mail: elena.s.green@nuim.ieThe Multifractal Model of Asset Returns (MMAR) was int roduced by Mandelbrot et al. [24] as an explanat ion of t he volat ility clust ers in financial dat a and t o include "out liers", large deviat ions which make up t he fat t ails of t he ret urn dist ribut ion. T he MMAR was present ed as an alt ernat ive t o Aut oregressive Condit ional Het eroscedast icity (ARCH) models which were int roduced by Engle [25] t o account for volat ility clust er...

The multifractal spectrum f(alpha) characterizing the scaling properties of the growth probability on the boundary of radial diffusion-limited aggregates is known to exhibit strong finite size effects. We demonstrate that there exists a correlation between these finite size effects and those present in measurements of the angular width of the fjords which lie between the principal cluster arms. We subsequently conclude that it is the evolution in the global structure of the clusters which is responsible for the slow convergence in f(alpha) and discuss how this global structure induces a phase transition in f(alpha).

The multifractal formalism is applied to the energy eigenvalues of Ce I, Ce II, Nd II, Sm I, Sm II, and Tb I. The Rényi dimensions D q , mass exponents τ (q) and f (α) spectra are calculated and used to characterize the eigenvalue spectra. It is found that these elements show multi-scaling behaviour that can be accurately modelled by simple multifractal recursive Cantor sets. The effect of unfolding the spectra is also investigated.

We examine the branch structure of radial diffusion-limited aggregation (DLA) clusters for evidence of multifractality. The lacunarity of DLA clusters is measured and the generalized dimensions D(q) of their mass distribution is estimated using the sandbox method. We find that the global n-fold symmetry of the aggregates can induce anomalous scaling behavior into these measurements. However, negating the effects of this symmetry, standard scaling is recovered.