Boltzmann and the Statistical Multifractals

[1]T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B. I. Shraimar (1986). Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. A 33, 1141-1151.HalseyT.C.JensenM.H.KadanoffL.P.ProcacciaI.ShraimarB. I.1986Fractal measures and their singularities: The characterization of strange setsPhys. Rev. A3311411151Search in Google Scholar

[2]Ludwig Boltzmann (1964). Lectures in gas theory. Dover Publications.BoltzmannLudwig1964Lectures in gas theoryDover PublicationsSearch in Google Scholar

[3]Radu Balescu (1975). Equilibrium and nonequilibrium statistical mechanics. John Wiley and Sons.BalescuRadu1975Equilibrium and nonequilibrium statistical mechanicsJohn Wiley and SonsSearch in Google Scholar

[4]H.G. Eggleston (1949). The fractional dimension of a set defined by the decimal properties. Quart.J.Math., Oxford Ser.20, 31-36.EgglestonH.G.1949The fractional dimension of a set defined by the decimal propertiesQuart.J.Math.Oxford Ser.203136Search in Google Scholar

[5]Yakov Pesin and Vaughn Climenhaga (2009). Lectures on fractal geometry and dynamical systems, American Mathematical Society. A discussion on the pointwise dimension is found in Lecture 16 page 123.PesinYakovClimenhagaVaughn2009Lectures on fractal geometry and dynamical systems, American Mathematical SocietyA discussion on the pointwise dimension is found in Lecture16123Search in Google Scholar

[6]Patrick Billingsley (1965). Ergodic Theory and Information. John-Wiley.BillingsleyPatrick1965Ergodic Theory and InformationJohn-WileySearch in Google Scholar

[7]Jens Feder (1988). Fractals. Plenum Press. section 6.6.FederJens1988FractalsPlenum Presssection 6.6Search in Google Scholar

[8]C. Beck and F. Schlögl (1993). Thermodynamics of chaotic systems. Cambridge University Press.BeckC.SchlöglF.1993Thermodynamics of chaotic systems.Cambridge University PressSearch in Google Scholar

[9]B.B. Mandelbrot(1983). The Fractal Geometry of Nature, Freeman and Co. New York, 376-379.MandelbrotB.B.1983The Fractal Geometry of NatureFreeman and Co.New York376379Search in Google Scholar

[10]B.B. Mandelbrot (1974). Intermittent turbulence in self-similar cascades: divergence in of high moments and dimension of the carrier. J. of Fluid Mechanics 62 331-358.MandelbrotB.B.1974Intermittent turbulence in self-similar cascades: divergence in of high moments and dimension of the carrierJ. of Fluid Mechanics62331358Search in Google Scholar

[11]A. Chhabra and R.V. Jensen (1989). Direct determination of the f(α) Singularity spectrum. Phys. Rev. Lett. 62 12, 1327-1330.ChhabraA.JensenR.V.1989Direct determination of the f(α) Singularity spectrumPhys. Rev. Lett.621213271330Search in Google Scholar

[12]J.L. Río-Correa and J. López-García (2012). Shannon Entropy and Hausdorff Dimension in Multifractals. Rev. Mex. Fis S 58 (1) 13-20.Río-CorreaJ.L.López-GarcíaJ.2012Shannon Entropy and Hausdorff Dimension in MultifractalsRev. Mex. FisS 5811320Search in Google Scholar

[13]P. Billingsley (1960) Hausdorff Dimension in Probability Theory I, Illinois Journal of Mathematics, Vol. 4, 187-209.BillingsleyP.1960Hausdorff Dimension in Probability Theory IIllinois Journal of Mathematics4187209Search in Google Scholar

[14]P. Billingsley (1961) Hausdorff Dimension in Probability Theory II, Illinois Journal of Mathematics, Vol. 5, No. 2, 291-298.BillingsleyP.1961Hausdorff Dimension in Probability Theory IIIllinois Journal of Mathematics52291298Search in Google Scholar