Discrete Scale Invariance & Complex Exponents

W.-X. Zhou and D. Sornette, Numerical investigations of descrete scale invariance in fractals and multifractal measures, Physica A 388, 2623-2639 (2009)
(http://arXiv.org/abs/cond-mat/0408600)

Wei-Xing Zhou and Didier Sornette, Renormalization Group Analysis of the 2000-2002 anti-bubble in the US S&P 500 index: Explanation of the hierarchy of 5 crashes and Prediction, Physica A 330, 584-604 (2003)
(http://arXiv.org/abs/physics/0301023)

Wei-Xing Zhou, Didier Sornette and Vladilen Pisarenko New Evidence of Discrete Scale Invariance in the Energy Dissipation of Three-Dimensional Turbulence: Correlation Approach and Direct Spectral Detection, Int. J. Modern Phys. C 14 (4), 459-470 (2003)
(http://arXiv.org/abs/cond-mat/0208347)

Wei-Xing Zhou and Didier Sornette, Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes, Int. J. Mod. Phys. C 14 (8), 1107-1126 (2003)
(http://arXiv.org/abs/cond-mat/0205531)

Wei-Xing Zhou and Didier Sornette, Generalized q-Analysis of Log-Periodicity: Applications to Critical Ruptures, Phys. Rev. E - art. no. 046111, 6604 N4 PT2:U129-U136 (2002)
(http://arXiv.org/abs/cond-mat/0201458)

S. Gluzman and D. Sornette, Log-periodic route to fractal functions,
art. no. 036142, Phys. Rev. E V6503 N3 PT2A:U418-U436 (2002)
(http://arXiv.org/abs/cond-mat/0106316)

Wei-Xing Zhou and Didier Sornette, Evidence of Intermittent Cascades
from Discrete Hierarchical Dissipation in Turbulence,
Physica D 165, 94-125 (2002)
(http://arXiv.org/abs/cond-mat/0110436)

Wei-Xing Zhou and Didier Sornette, Statistical Significance of
Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise,
Int. J. Mod. Phys. C 13 (2), 137-170 (2002)
(http://arXiv.org/abs/cond-mat/0110445)

D. Sornette and K. Ide, Theory of self-similar oscillatory finite-time singularities in Finance, Population and Rupture, Int. J. Mod. Phys. C 14 (3), 267-275 (2002)
(http://arXiv.org/abs/cond-mat/0106054)

K. Ide and D. Sornette,Oscillatory Finite-Time Singularities in Finance, Population and Rupture, Physica A 307 (1-2), 63-106 (2002)
(http://arXiv.org/abs/cond-mat/0106047)

J.-C. Anifrani, C. Le Floc'h and D. Sornette, Prediction de la rupture de reservoirs composites de haute pression a l'aide de l'emission acoustique, Controle Industriel 220, 43-45 (1999)

G. Ouillon and D. Sornette, The Concept of `critical earthquakes' applied to mine rockbursts with time-to-failure analysis, Geophys. J. Int. 143, 454-468 (2000)

Y. Huang, H. Saleur and D. Sornette, Reexamination of log-periodicity observed in the seismic precursors of the 1989 Loma Prieta earthquake, J. Geophysical Research 105, B12, 28111-28123 (2000)
(http://arXiv.org/abs/physics/0007095)

Y. Huang, A. Johansen, M.~W. Lee, H. Saleur and D. Sornette, Artifactual Log-Periodicity in Finite-Size Data: Relevance for Earthquake Aftershocks, J. Geophys. Res. 105, 25451-25471 (2000)
(http://xxx.lanl.gov/abs/cond-mat/9911421)

A. Johansen, H. Saleur and D. Sornette, New Evidence of Earthquake Precursory Phenomena in the 17 Jan. 1995 Kobe Earthquake, Japan, Eur. Phys. J. B 15, 551-555 (2000)
(http://xxx.lanl.gov/abs/cond-mat/9911444)

M.W. Lee and D. Sornette, Novel mechanism for discrete scale invariance in sandpile models, European Physical Journal B 15, 193-197 (2000)
(http://xxx.lanl.gov/abs/cond-mat/9903402)

A. Johansen, D. Sornette and A.E. Hansen, Punctuated vortex coalescence and discrete scale invariance in two-dimensional turbulence, Physica D 138, Issue 3-4, pp. 302-315 (15 April 2000)
(http://xxx.lanl.gov/abs/cond-mat/9902247)

A. Johansen and D. Sornette, Evidence of discrete scale invariance by canonical averaging, Int. J. Mod. Phys. C 9, 433-447 (1998)
(http://xxx.lanl.gov/abs/cond-mat/9803191)

D. Sornette, Discrete scale invariance in turbulence? in the Proceedings of the Seventh European Turbulence Conference (ETC-7), June 30-July 3 (1998) (Published by Kluwer, U. Frisch, editor)
(http://xxx.lanl.gov/abs/cond-mat/9802121)

D. Stauffer and D. Sornette, Log-periodic Oscillations for Biased Diffusion on 3D Random Lattice, Physica A 252, 271-277 (1998)
(http://xxx.lanl.gov/abs/cond-mat/9712085)

D. Sornette, Discrete scale invariance and complex dimensions, Physics Reports 297, 239-270 (1998)
(http://xxx.lanl.gov/abs/cond-mat/9707012)

Per Jogi, Didier Sornette and Michael Blank, Fine structure and complex exponents in power law distributions from random maps, Phys. Rev. E 57 120-134 (1998)
(http://xxx.lanl.gov/abs/cond-mat/9708220)

D. Sornette, Generic mechanisms for hierarchies, InterJournal Complex Systems, 129, Manuscript Number: [129], Submission Date: 971015, Subject(s): CX.08, CX.01
(http://www.ji.si.ehu.es/Activities/Sc/sornegmh.htm)
Proceedings of the New England Complex Systems, Institute Conference, Nashua, Newhampshire, Y. Bar-Yam (ed.), (1997)

Huang, G. Ouillon, H. Saleur and D. Sornette, Spontaneous generation of discrete scale invariance in growth models, Physical Review E 55, N6, 6433-6447 (1997).

A. Johansen, D. Sornette, H. Wakita, U. Tsunogai, W.I. Newman and H. Saleur, Discrete scaling in earthquake precursory phenomena : evidence in the Kobe earthquake, Japan, J.Phys.I France 6, 1391-1402 (1996)

G. Ouillon, D. Sornette, A. Genter and C. Castaing, The imaginary part of rock jointing, J. Phys. I France 6 (8), 1127-1139 (1996)

H. Saleur, C.G. Sammis and D. Sornette, Discrete scale invariance, complex fractal dimensions and log-periodic corrections in earthquakes, Journal of Geophysical Research-Solid Earth 101, NB8, 17661-17677 (1996 AUG 10)

H. Saleur, C.G. Sammis and D. Sornette, Renormalization group theory of earthquakes, Nonlinear Processes in Geophysics 3, No. 2, 102-109 (1996)

H. Saleur and D. Sornette, Complex exponents and log-periodic corrections in frustrated systems, J.Phys.I France 6, n3, 327-355 (1996)

D. Sornette, A. Johansen, A. Arneodo, J.-F. Muzy and H. Saleur, Complex fractal dimensions describe the internal hierarchical structure of DLA, Phys. Rev. Lett. 76, 251-254 (1996)

J.-C. Anifrani, C. Le Floc'h, D. Sornette and B. Souillard, Universal Log-periodic correction to renormalization group scaling for rupture stress prediction from acoustic emissions, J.Phys.I France 5 (6) 631-638 (1995)

D. Sornette and C.G. Sammis, Complex critical exponents from renormalization group theory of earthquakes : Implications for earthquake predictions, J.Phys.I France 5, 607-619 (1995)