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Literaturverzeichnis Literaturverzeichnis Jede Literaturangabe in diesem Verzeichnis enthält den ALEXANDER, S. S. (1964). Price movements in speculative Namen des Autors oder des Herausgebers sowie eine markets: No. 2. Industrial Management Review of Jahreszahl. Eine mit- versehene Jahresangabe verweist M.I. T. 4, Part 2, 25-46. Nachdruck in CooTNER, P. H. auf den ersten Band einer Sammlung. Falls notwendig, (Hrsg.) (1964), 338-372. folgt der Jahreszahl noch ein Buchstabe, der meist vom * ALEXANDER, S. & ÜRBACH, R. (1982). Density of states on Titel der Publikation oder dem Namen der Zeitschrift fractals: «fractons». Journal de Physique Lettres 43, abgeleitet ist. Diese neue Bezeichnungsweise soll das Ar­ 625. beiten erleichtern. ALLEN, J. P., COLVIN, J. T., STINSON, D. G., FLYNN, c. P. & Da die aufgeführten Zeitschriften zu sehr unterschied­ STAPLETON, H. J. (1981). Protein conformation from lichen Wissensgebieten gehören, wurden die Titel weni­ electron spin relaxation data (Preprint). Champaign, ger abgekürzt als üblich. Auf allgemeine Literatur ist im Illinois. Verzeichnis fast völlig verzichtet worden. Außerdem *ANDREws, D. J. (1980-81). A stochastic fault model. wurde weder ein ausgewogenes Verhältnis noch eine I Static case, II Time-rlependent case. Journal of vollständige Überdeckung der verschiedenen in diesem Geophysical Research 85B, 3867-3877; 86B, Werk angesprochenen Gebiete angestrebt. 10821-10834. Ergänzungen des Autors wurden mit * bzw. (*)(siehe APosTEL, L., MANDELBROT, B. & MoRF, A. (1957). Logique, Nachtrag, S. 432) markiert, Zusätze des Herausgebers Iangage et theorie de l'information. Paris: Presses Uni­ der deutschen Übersetzung mit **. versitaires de France. ARTHUR, D. W. G. (1954). The distribution of lunar cra­ ABBoT, L. F. & WisE, M. B. (1981). Dimension of a quan­ ters. J. of the British Astronomical Association 64, tum-mechanical path. American J. of Physics 49, 127-132. 37-39. AusRY, S. (1981 ). Many defect structures, stochasticity and ABELL, G. 0. (1965). Clustering of galaxies. Annual Re­ incommensurability. Les Hauches 1980. Hrsg. R. BA. views ofAstronomy and Astrophysics 3, 1-22. LIAN & M. KLEMAN. New York: North-Holland, 1981. ADLER, R. J. (1981). The geometry ofrandomfields. New **AvNIR, D., FARIN, D. & PFEIFFER, P. (1985). Surface York: Wiley. geometric irregularity of particular materials: The (*) AGTENBERG, F. P. ( 1982). Recent developments in geo­ factal approach. J. of Colloid and Interface Science mathematics. Geo-processing 2. 103, 112-123. ALEXANDER, S. S. (1961). Price movements in speculative AvRoN, J. E. & SIMON, B. (1981). Almost periodic Hill's markets: or random walks. Industrial Management equation and the rings of saturn. Physical Review Let­ Review of M. I. T. 2, Part 2, 7-26. Nachdruck in CooT­ ters 46, 1166-1168. NER, P. H. (Hrsg.) (1964), 199-218. AzBEL, M. JA. (1964). Energy spectrum of a conduction electron in a magnetic field. Soviet Physics JETP 19, 634-645. 442 Literaturverzeichnis BAcHELIER, L. (1900). Theorie de Ia speculation. Disserta­ BERRY, M. V. & HANNAY, J. H. (1978). Topography ofran­ tion in den mathematischen Wissenschaften (vertei­ dom surfaces. Nature 273, 573. digt am 29. März 1900). Annales Scientifiques de ßERRY, M. V. & LEwis, Z. V. (1980). On the Weierstrass­ l'Ecole Normale Superieure 111-17, 21-86. Eng!. Mandelbrot fractal function. Pr. of the Royal Society Übers. in CooTNER, P. H. (Hrsg.) (1964), 17-78. London A370, 459-484. BACHELIER, L. (1914). Lejeu, Ia chance et le hasard. Paris: BESICOVITCH, A. S. (1934). On rational approximation to Flammarion. real numbers. J. of the London Mathematica/ Society BALMINO, G., LAMBECK, K. & KAULA, w. M. (1973). A 9, 126-131. spherical harmonic analysis of the Earth's topogra­ ßEsicovncH, A. S. (1935). On the sum of digits of real phy. J. of Geophysical Research 78, 478-481. numbers represented in the dyadic system (On sets of BARBER, M. N. & NINHAM, B. W. (1970). Random andres­ fractional dimensions II). Mathematische Annalen tricted walks: theory and applications. New York: Gor­ 110, 321-330. don & Breach. ßESicovncH, A. S. & TAYLOR, S. J. (1954). On the comple­ *BARNSLEY, M. F. & DEMKO, S. (1987). Chaotic Dynamics mentary interval of a linear closed set of zero Le­ and Fractals. Orlando, FL: Academic Press. besgue measure. J. ofthe London Mathematica/ Socie­ **BARNSLEY, M. F., ÜERONIMO, J. s. & HARRINGTON, A. N. ty29, 449-459. (1985). Condensed Julia sets, with an application to a ßESICOVITCH, A. S. & URSELL, H. D. (1937). Sets of frac­ fractallattice model Hamiltonian. Tr. ofthe American tional dimensions (V): On dimensional numbers of Mathematical Society288, 537-561. some continuous curves. J. ofthe London Mathemati­ BARRENBLATT, G. I. (1979). Similarity, self-similarity, and cal Society 12, 18-25. intermediate asymptotics. New York: Plenum. ßEYER, W. A. ( 1962). Hausdorff dimension of Ievel sets of BARTLETT, J. (1968). Familiar quotations (14. Aufl.) Bos­ some Rademacher series. Pacific J. of Mathematics ton: Little Brown. 12,35-46. BATCHELOR, G. K. (1953). The theory of homogeneaus **BEYER, w. A., MAULDIN, R. D. & STEIN, P. R. (1986). turbulence. Cambridge University Press. Shirt-maximal sequences in function iteration: exis­ BATCHELOR, G. K. & TowNSEND, A. A. (1949). The nature tence, uniqueness, and multiplicity. J. of Mathemati­ of turbulent motion at high wave numbers. Pr. of the cal Analysis and Applications 115, 305-362. Royal Society of London A 199, 238-255. BIDAUX, R., ßOCCARA, N., SARMA, G., SEZE, L., DE ÜENNES, BATCHELOR, G. K. & TowNsEND, A. A. (1956). Turbulent P. G. & PARODI, 0. (1973), Statistical properties of fo­ diffusion. Surveys in Mechanics. Hrsg. G. K. BATCH& cal conic textures in smectic liquid crystals. Le J. de LOR & R. N. DAviEs. Cambridge University Press. Physique 34, 661-672. **BEDFORD, T. (1986). Dimension and dynamics for frac­ BIENAYME, I. (1853). Considerations a I'appui de Ia de­ tal recurrent sets. J. London Math. Soc. (2) 33,89-100. couverte de Laplace sur Ia loi de probabilite dans Ia BERGER, J. M. & MANDELBROT, B. B. (1963). A new model methodedes moindres carres. Comptes Rendus(Paris) for the dustering of errors on telephone circuits. IBM 37, 309-329. J. of Research and Development 7, 224-236. ßiLLINGSLEY, P. (1967). Ergodie theory and information. BERMAN, S. M. (1970). Gaussian processes with station­ New York: Wiley. ary increments: local times and sample function pro­ BILLINGSLEY, P. (1968). Convergence of probability mea­ perties. Annals of Mathematical Statistics 41, sures. New York: Wiley. 1260-1272. BIRKHOFF, G. (1950-1960). Hydrodynamics (!. und BERRY, M. V. (1978). Catastrophe and fractal regimes in 2. Aufl.). Princeton University Press. random waves & Distribution of nodes in fractal res­ (*)BLEI, R. (1983). Combinatorial dimension: a continu­ onators. Structural stability in physics. Hrsg. W. GOT­ ous parameter. Symposia Mathematica (Italien). TINGER & H. EIKEMEIER. New York: Springer. BLUMENTHAL, L. M. & MENGER, K. (1970). Studies in BERRY, M. V. (1979). Diffractals. J. of Physics A12, geometry. San Francisco: W. H. Freeman. 781-797. Literaturverzeichnis 443 BLVMENTHAL, R. M. & GETOOR, R. K. (1960c). A dimen­ BRODMANN, K. (1913). Neue Forschungsergebnisse der sion theorem for sample functions of stable processes. Grassgehirnanatomie . Verhandlungen der 85. Ver­ Illinois J. of Mathematies4, 308-316. sammlung deutscher Naturforscher und Xrzte in Wien, BLVMENTHAL, R. M. & GETOOR, R. K. (1960m). Some the­ 200-240. orems on stable processes. Tr. ofthe American Mathe­ BROLIN, H. (1965). Invariant sets under iteration of ra­ matical Soeiety 95, 263-273. tional functions. Arkiv för Matematik6, 103-144. BLUMENTHAL, R. M. & GETOOR, R. K. (1962). The dimen­ **BROOMHEAD, D. S. & RowLANDS, G. (1984). On the use sion of the set of zeros and the graph of a symmetric of perturbation theory in the calculation of the fractal stable process. Iilinois J. of Mathematies6, 370-375. dimension of strange attractors. Physica D 10, BocHNER, S. (1955). Harmonie ana/ysis and the theory of 340-352. probability. Berkeley: University of California Press. BROUWER, L. E. J. (1975-). Collected works. Hrsg. A. HEY· BoND!, H. (1952); Cosmology. Cambridge University TING & H. FREUDENTHAL. New York: Elsevier North Press. Holland. BoREL, E. (1912-1915). Les theories moleculaires et !es BROWAND, F. K. (1966). An experimental investigation of mathematiques. Revue Generale des Seiences 23, the instability of an incompressible separated shear 842-853. Übersetzt als Molecular theories and mathe­ layer. J. Fluid Mechanies 26, 281-307. matics. Rice Institute Pamphlet 1, 163-193. Nach­ BROWN, G. L. & RosHKO, A. (1974). On density effects and druck in BoREL, E. (1972-,), III, 1773-1784. !arge structures in turbulent mixing Iayers. J. of Fluid BoREL, E. (1922). Definition arithmetique d'une distribu­ Mechanies 64, 775-816. tion de masses s'etendant a l'infini et quasi peri­ BRUSH, S. G. (1968). A history of random processes. I. odique, avec une densite moyenne nulle. Comptes Brownian movement from Brown to Perrin. Archive Rendus (Paris) 174, 977-979. for History of Exact Seiences 5, 1-36. BoREL, E. (1972-). Oeuvres de Emile Bore/. Paris: Edi­ *BURKS, A. W. (Hrsg.) (1970). Essays on Cel/ular Automa­ tions du CNRS. ta. Urbana, IL: University of Illinois Press. BouuGAND, G. (1928). Ensembles impropres et nombre (*)BuRROUGH, P. A. (1981). Fractal dimensions ofland­ dimensionnel. Bulletin des Seiences Mathematiques scapes and other environmental data. Nature 294, 11-52, 320-334; 361-376. 240-242. BouLIGAND, G. (1929).
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