Laurent Nottale
List of publications about:
"Scale Relativity, nondifferentiable
geometry and fractal space-time".
Chronological order. April 2006.
(see page "downloable papers" for complete
links)
Nottale, L., Schneider, J., 1984, J. Math. Phys., 25, 1296.
"Fractals and Non-Standard Analysis".
Nottale, L., 1988, C. R. Acad. Sc. Paris, 306, 341
"Sur le temps de la microphysique".
Nottale, L., 1989, International Journal of Modern Physics,
A4,
5047-5117
"Fractals and the Quantum Theory of Space-Time".
Nottale, L., 1990, in "Particle Astrophysics: The early Universe and Cosmic
Structures", 10th Moriond Astrophysics meeting, eds. A. Blanchard and J.
Tran Thanh Van (Frontières), p. 13.
"The fractal structure of the quantum space-time".
Nottale, L., 1990, in "Applying Fractals in Astronomy", 2th Journées
de Strasbourg, Eds. A. Heck and J. Perdang (Springer-Verlag), p. 181.
"The Fractal Structure of the Quantum Space-Time".
Nottale, L., 1991, in "Progress in Electromagnetics Research Symposium",
Proceedings (Cambridge, USA), p. 754.
"Fractals and Quantum Theory of Space-Time".
Nottale, L., 1992, International Journal of Modern Physics A7,
4899-4936 --> Version PDF
"The Theory of Scale Relativity".
Nottale, L., 1992, invited conference, DISTANCIA'92, International Meeting
on Distance Analysis (Rennes, France), S. Joly & G. Le Calvé
eds., Université de Rennes, p.317.
"Distances et Relativité"
BOOK:
Nottale,
L., 1993, (World Scientific, 1993), 333 pp.
"Fractal Space-Time and Microphysics:
Towards a Theory of Scale Relativity."
For an on-line version (© World
Scientific) of Chapter 1 (Introduction) and Chapter 2 (Relativity and
Quantum Physics), click here.
For the list of references of the book (alphabetical
order): references.
Nottale, L., 1993, in "Cellular Automata: Prospects in Astrophysical Applications"
, Université de Liège, A. Lejeune and J. Perdang (eds.),
(World Scientific, 1993), pp.268-277.
"Emergence of structures from chaos."
Nottale, L., 1994, Chaos, Solitons & Fractals, 4, 361-388.
Reprinted in "Quantum Mechanics, Diffusion and Chaotic Fractals", Eds.
M.S. El Naschie, O.E. Rössler and I. Prigogine (Pergamon, 1995), p.51
---> Version PDF
"Scale-Relativity, Fractal Space-Time and Quantum Mechanics".
Nottale, L., 1994, invited conf., "First International Conference on Complex
Systems in Computational Physics", Buenos-Aires, Ed. Marshall (Pergamon),
Chaos,
Solitons & Fractals 6, 401. ---> Version
PDF
"Scale-Relativity: From Quantum Mechanics to Chaotic Dynamics".
Nottale, L., 1994, invited conference in "Relativity in General", E.R.E.
93 (Spanish Relativity Meeting) Salas, Ed. J. Diaz Alonso and M. Lorente
Paramo (Frontières), p.121. ---> Version
PDF
"Scale-Relativity: First Steps toward a Field Theory".
Nottale, L., 1994, in "Le Big-Bang en question", Science et Vie Hors
Série, 189, 116
"Univers Primordial et Relativité d'Echelle". (in French)
Nottale, L., 1995, invited conference in "Chaos and diffusion in Hamiltonian
systems", (Chamonix, Février 1994), Ed. D. Benest et C. Froeschlé
(Frontière), pp 173-198. ---> Version
PDF
"New Formulation of Stochastic Mechanics. Application to Chaos".
Nottale, L., 1995, in "Fractal Reviews in the Natural and Applied Sciences",
Proceedings of "Fractals'95", Ed. M.M. Novak, (Chapman & Hall, London,
1995), pp. 12-23.
"Scale Relativity: Many-Particle Schrödinger Equation".
Nottale, L., 1995, Pour la Science, 215, 34 (Septembre 1995)
"L'Espace-Temps Fractal".
Nottale, L., 1995, in "Clustering in the Universe", 15th Moriond Astrophysics
meeting, eds. S. Maurogordato, C. Balkowski, C. Tao and J. Tran Thanh Van
(Frontières), p. 523 ---> Version
PDF
"Scale Relativity and Structuration of the Universe".
Review paper:
Nottale, L., 1996, Chaos, Solitons and Fractals,
7, 877-938
"Scale Relativity and Fractal Space-Time: Application
to Quantum Physics, Cosmology and Chaotic systems". -->
PostScript
version ---> PDF
version
Nottale, L., 1996, Astron. Astrophys. Lett., 315, L9
"Scale relativity and quantization of extrasolar planetary systems".
--> pdf version
Nottale, L., and Schumacher, G., Gay, J., 1997, Astron. Astrophys.,
322,
1018-1025
"Scale relativity and quantization of the Solar System". --> pdf
version
Nottale, L., 1997, Astron. Astrophys., 327, 867
"Scale relativity and quantization of the universe. I. Theoretical
framework" --> ps version --> pdf
version
Nottale, L., 1997, in "Scale invariance and beyond", proceedings of Les
Houches school, Ed. B. Dubrulle, F. Graner and D. Sornette, (EDP Sciences
/Springer), p. 249.
Nottale, L., 1997, in Proceedings of I.A.C. colloquium, Paris 8 University,
Intelligence artificielle et complexité, Ed. A. Ali Cherif et J.
Signorini, p. 66
"La relativité d'échelle".
Nottale, L., 1997, in "Planetary systems: the long view", Proceedings of
IXè rencontres de Blois, , Eds. L. Celnikier et J. Tran Thanh Van,
Frontières, p. 51
"Scale-relativity and universal structures in planetary systems".
Nottale, L., 1997, in Les Trous Noirs, Pour la Science (Dossier hors série),
p.57.
"Sommes-nous dans un trou noir ?".
Nottale, L., 1997, in Proceedings of Institute Kurt Bösch workshop,
"Emergence, Entropy and the Creative Universe", Ed. T. Bernold, p. 155.
"The scale-relativistic view of the world".
Nottale, L., 1997, in Proceedings of Colloquium "Dimension", Maison des
Sciences de l'Homme, Eds. D. Flament, Chap. VIII.
"Dimension fractale et relativité d'échelle".
Nottale, L., 1998, Ciel et Terre, Bulletin de la Société
royale belge d'Astronomie, vol 114 (2), 63-71.
"Relativité d'échelle et cosmologie".
Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1035
"Scale relativity and quantization of planet obliquities".
Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1043
"Scale Relativity and Quantization of the Planetary System around the
pulsar PSR B1257+12 ".
Nottale, L., 1998, Chaos, Solitons and Fractals, 9, 1051
"Scale relativity and Schrödinger's equation".
Nottale, L. & Schumacher G., 1998, in "Fractals and beyond : Complexities
in the Sciences", Proceedings of 'Fractal 98' conference, (World Scientific),
Ed. M.M. Novak, p. 149.
"Scale relativity, fractal space-time and gravitational structures".
--> pdf version
BOOK (in french):
Nottale, L., 1999, Chaos, Solitons and Fractals, 10, 459 (special issue)
"The Scale-Relativity Program".
Nottale, L., 1999, Proceedings of I.A.C.'98 colloquium, Paris 8 University,
Intelligence artificielle et complexité, Eds. A. Ali Cherif et J.
Signorini, p. 51
"Relativité d'échelle et structuration gravitationnelle".
Chaline, J., Nottale, L., Grou, P., 1999, C.R. Acad. Sci. Paris, 328, 717
"Is the evolutionary tree a fractal structure ?"
Chaline J., Nottale L. et Grou P., 1999, C. R. Acad. Sci. Paris, 328, IIa,
717-726.
"Réponse au commentaire de Eric Buffetaut au "Point sur" L'arbre
de la vie a-t-il une structure fractale ?"
Nottale, L., 1999, La Mazarine, Oct. 1999, 10, p. 21.
"Relativité restreinte d'échelle et cosmologie".
Nottale, L., Schumacher, G., & Lefèvre, E.T., 2000, Astron.
Astrophys. 361, 379
Nottale, L., Galopeau, P.H.M., & Lefèvre, E.T., 2000, Physics
and Chemistry of the Earth, preprint
"Scale relativity and quantization of planetary systems".
Nottale, L., 2000, Proceedings of 4è Forum Halieumétrique
(Juin 1999), Les espaces de l'halieutique, Eds. D. Gascuel, P. Chavance,
N. Bez & A. Biseau, IRD Editions, p.41
"La théorie de la relativité d'échelle: réflexions
pour une application à l'halieutique"
Nottale, L., 1999, in Temps, an 2000, ed. Desjeunes
"De la relativité du mouvement à la relativité
d'échelle".
Nottale, L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars
2001, p. 11-25
"Relativité d'échelle: structure de la théorie".
Nottale, L., 2001, Revue de Synthèse, T. 122, 4e S., N°1, janvier-mars
2001, p. 93-116
"Relativité d'échelle et morphogénèse".
--> pdf version
Nottale, L., 2000, in Séminaire "Histoires de géométries",
Maison des sciences de l'homme, Ed. D. Flament, p.1
"Espace-temps fractal et mécanique quantique".
Nottale, L., 2000, in Science of the Interface, Proceedings of International
Colloquium in honor of Otto Rössler, ZKM Karlsruhe, 18-21 May 2000,
Eds. H. Diebner, T. Druckney and P. Weibel, p. 38 (Genista Verlag, Tübingen,
2001)
Nottale, L., Chaline, J., & Grou, P. 2000, in "Fractals in Biology
and Medicine", Proceedings of Fractal 2000 Third International Symposium,
Ed. G. Losa, Birckhäuser Verlag, p. 247
"On the fractal structure of evolutionary trees". ---> PDF
version
-
BOOK (in french)
Nottale, L., Chaline,
J., & Grou, P., (Hachette Littératures, Mars 2000), 380pp.
"Les arbres de l'évolution: Univers, Vie, Sociétés".
Nottale, L., 2001, in Frontiers of Fundamental Physics, Proceedings of
Birla Science Center Fourth International Symposium, 11-13 dec. 2000, Hyderabad,
India, Eds. B.G. Sidharth and M.V. Altaisky, (Kluwer Academic), p. 65.
--> version ps --> version
pdf
"Scale relativity and non-differentiable fractal space-time".
Nottale, L., 2002, in Traité IC2, "Lois d'échelle, fractales
et ondelettes", eds. P. Abry, P. Gonçalvès et J. Levy Vehel,
(Hermès 2002), Vol. 2, Chap. 7, p. 233
"Relativité d'échelle, nondifférentiabilité
et espace-temps fractal". --> pdf version
(in french)
Nottale, L., 1998-2002, Web pages, http://www.daec.obspm.fr/users/nottale/index.html
"Scale relativity and fractal space-time".
Nottale, L. & Tran Minh N., 2001, Actualités / Nouvelles Scientifiques,
Observatoire de Paris, Mai 2001, http://www.obspm.fr/actual/nouvelle/nottale/nouv.fr.shtml
"Prédiction des orbites des planètes et exoplanètes".
Cash R., Chaline, J., Nottale, L., Grou, P., 2002, C.R. Biologies
325, 585-590
"Développement humain et loi log-périodique ".
Nottale L., 2002, invited conference in International Colloquium "Géométrie
au XXè siècle", Paris, 24-29 Septembre 2001 -->
Version
ps --> version pdf
"Non-differentiable space-time and scale-relativity".
Nottale, L., 2002, in Vè Symposium "Mathématiques et Dialyse"
(Pyramide du Louvre, Paris, 13 Novembre 2000), N.K. Man, B. Perrone, T.
Petitclerc coordonnateurs (Meditor, Strasbourg), p. 3.
"La flêche du temps en relativité d'échelle".
Nottale, L., 2002, in La complexité, vertiges et promesses, 18 histoires
de sciences (entretiens avec Morin, Prigogine, Gershensfeld, Mange, Deneubourg,
Steels, Langton, Varela, Goodwin, Kauffman, Derrida, Pomeau, Ekeland, Chaitin,
Barrow, Nottale, Linde, Serres), ed. Reda Benkirane, Le Pommier, Chap.
XVI, pp. 329-356
"La relativité d'échelle". (In French)
Nottale, L., 2002, in "Penser les limites. Ecrits en l'honneur d'André
Green", Delachiaux et Niestlé, p. 157.
"Relativité, être et ne pas être". (In French)
P. Galopeau, L. Nottale, D. Da Rocha, N. Tran Minh, C. Mégessier
et G. Schumacher, 2002, Actes du 3e Colloque du Programme National de Planétologie
de líINSU, eds. O. Grasset, A. Cossard et C. Sotin, pp. 18-19.
"Application de la relativité d'échelle aux planètes
extrasolaires"
Nottale, L., 2003, Chaos, Solitons and Fractals, 16, 539 -->
Version
ps --> Version pdf
"Scale-relativistic cosmology".
Da Rocha D. & Nottale, L., 2003, Chaos, Solitons and Fractals, 16,
565 --> Version pdf
"Gravitational structure formation in scale-relativity".
Nottale, L., 2003, Electromagnetic Phenomena, T. 3, N°1 (9), 24 -->
Version
ps --> pdf version
"Theory of Electron in Scale Relativity".
Célérier, M.N., Nottale, L., 2003, Electromagnetic Phenomena,
T. 3, N°1 (9), 83 (eprint hep-th/0210027)
"A scale-relativistic derivation of the Dirac equation".
Nottale, L., 2003, L'Astronomie 117,3
"Conséquences astrophysiques et cosmologiques de la théorie
de la relativité d'échelle".
Nottale, L., 2003, Pour La Science, 309, 38-45 (Juillet 2003)
"La relativité díéchelle à líépreuve
des faits".
Da Rocha D. & Nottale, L., 2003, in Colloquium "Winds, Bubbles,
and Explosions: a conference to honor John Dyson", Pátzcuaro, Michoacán,
México, September 9-13, 2002 (Eds. S. J. Arthur & W. J. Henney)
Revista Mexicana de Astronomía y Astrofísica (Serie de Conferencias)
Vol. 15, p. 69
"On the morphogenesis of planetary nebulae".
Nottale, L., 2003, Siècle 21 Littérature & société,
2è année n°2, pp. 149-154
"L'évolution du concept de temps en physique".
Nottale L., 2003, Science & Conscience 11, 62-67.
"De la relativité d'échelle à la réalité...".
Grou P., Nottale L., Chaline J., 2004, in "Zona Arqueologica, Miscelanea
en homenaje a Emiliano Aguirre", IV Arqueologia : 230-237, Museo Arquelogico
Regional, Madrid.
"Log-periodic laws applied to geosciences".
Célérier M.-N. & Nottale, L., 2004, J. Phys. A, 37, 931-955
"Quantum-classical transition in scale relativity".
Nottale L., 2004, invited conference, in "Computing Anticipatory Systems.
CASYS'03 - Sixth International Conference" (Liège, Belgique, 11-16
Août 2003), Daniel M. Dubois Editor, American Institute of Physics
Conference Proceedings 718, 68-95
"The Theory of Scale Relativity: Non-Differentiable Geometry
and Fractal Space-Time".
Nottale L, Galopeau P., Ceccolini D. Da Rocha D. Schumacher G. & Tran-Minh
N., 2004, in "Extrasolar Planets: Today and Tomorrow", XIXè colloque
IAP (Paris, France), 30 June-4 July 2003, Eds. J.P. Beaulieu, A. Lecavelier
and C. Terquem, ASP Conference Proceeding 321, 355
"Structuring of the semimajor axis and eccentricity distributions
of exoplanets"
Nottale L., 2005, invited contribution in the volume "Trends in Field Theory
Research", (Nova Science), in press
"Geometric interpretation of gauge fields in the theory of scale
relativity"
Nottale L., 2004, in G. Ord, P. Weibel, O. Rössler (Eds.) , Springer
Vienna, in press
"On the transition from the classical to the quantum regime in
fractal space-time theory".
Nottale L., 2004, Proceedings of Symposia in Pure mathematics, , 72, Part
1, p. 57 (American Mathematical Society, Providence)
"Fractal Geometry and the Foundations of Physics".
Nottale L., 2004, in "Scientific Highlights 2004", Proceedings of the Journées
de la SF2A, Paris 14-18 Juin 2004, F. Combes & D. Barret eds., EDP
Sciences, p. 373
"Energy structure at 3.2 10^20 eV in special scale-relativity"
Célérier M.N. & Nottale L., 2004, in "Scientific Highlights
2004", Proceedings of the Journées de la SF2A, Paris 14-18 Juin
2004, F. Combes & D. Barret eds., EDP Sciences, p. 649
"Generalized macroscopic Schrödinger equation in scale relativity"
Lehner T., Nottale L., di Menza L., da Rocha D., & Ceccolini D., 2004,
in "Scientific Highlights 2004", Proceedings of the Journées de
la SF2A, Paris 14-18 Juin 2004, F. Combes & D. Barret eds., EDP Sciences,
p. 687
"Structure formation by the Hartree equation"
Nottale L., 2004, in "Scientific Highlights 2004", Proceedings of
the Journées de la SF2A, Paris 14-18 Juin 2004, F. Combes &
D. Barret eds., EDP Sciences, p. 699
"Scale relativity and dark potential"
Galopeau P., Nottale L., Ceccolini D., da Rocha D., Schumacher G. &
Tran-Minh N., 2004, in "Scientific Highlights 2004", Proceedings of the
Journées de la SF2A, Paris 14-18 Juin 2004, F. Combes & D. Barret
eds., EDP Sciences, p. 75
"Distribution of orbital elements of planets and exoplanets in
scale relativity"
Nottale L., 2005, Progress in Physics, 1, 12-16
"Fractality field in the theory of scale relativity".
Auffray C., Nottale L. & the Systemoscope Consortium, Invited Conference
in International Conference "Integrative Systems Biology for Health - TRANSCRIPTOME
2005", Shanghai, Chine, 5-9 Novembre 2005
"Scale Relativity in Systems Biology of Muscular and Pulmonary
Diseases"
Nottale L., Célérier M.N., Lehner T., 2006, J. Math. Phys.
47, 032303 (eprint hep-th/0307093)
"Non-Abelian gauge field theories in scale relativity".
Nottale L. 2006, in Proceedings of 7th International Colloquium on Clifford
Algebra, Ed. P. Anglès (Birkhauser, 2006)
"Origin of complex and quaternionic wavefunctions in quantum
mechanics: the scale-relativistic view".
Nottale L. 2006, Invited Conference in "Frontiers of Fundamental Physics",
Proceedings of the Sixth International Symposium "Frontiers of Fundamental
and Computational Physics", Udine, Italy, 26-29 September 2004, Sidharth,
B.G., Honsell, F. & de Angelis, A. (Eds.)
"Astrophysical applications of the theory of scale relativity".
Nottale L. 2006, Invited Conference, Proceedings du Congrès FFN,
Paris 2005, sous presse
"Analyse temporelle de phénomènes de crise: lois
d'évolution log-périodique"
Others publications about scale
relativity (not exhaustive)
Ben Adda F. and Cresson J., 2000, C. R. Acad. Sci. Paris, 330, Série
I, p. 261
"Divergence d'échelle et différentiabilité"
Ben Adda F. and Cresson J., 2001, Journ. Mathematical Analysis and
Applications 263, 721
"About non-differentiable functions"
Castro, C., Foundations of Physics Lett., 10, 273
"String theory, scale relativity and the generalized uncertainty principle"
Castro, C., preprint hep-th/9612003
"Incorporating the scale-relativity principle in string theory and
extended objects"
Cresson J., 2002, Chaos Solitons and Fractals 14, 553
"Scale relativity theory for one dimensional non differentiable
manifold"
Dubrulle, B. & Graner F., 1996, J. Phys. II (Fr) 6, 797.
"Possible Statistics of Scale Invariant Systems"
Altaisky, M.V., 1996, Differential Equations and Dynamical Systems,
Vol. 4, N. 3/4, 267
"On some geometrical consequences of the incorporation of resolution
in the definition of a coordinate system"
Hermann,
R. P., 1997, J. Phys. A30, 3967-3975, 1997
"Numerical simulation of a quantum particle in a box"
Herrmann,
F., 1997, Ph.D. Thesis, Delft University of Technology, The Netherlands
"A scaling medium representation, a discussion on well-logs, fractals
and waves" (see in particular the Epilogue)
Hermann R., Schumacher G., Guyard R., 1998, Astron. Astrophys. 335,
284 (PDF)
"Scale relativity and quantization of the solar system. Orbit
quantization of the planetís satellites"
Laperashvili L.V., Ryzhikh D.A., 2001, arXiv:hep-th/0110127
"Phase transition in Gauge Theories and the Planck Scale Physics"
Pissondes, J.C., 1999, Chaos, Solitons and Fractals 10, 513
"Covariance in general relativity and scale-covariance in scale-relativity,
quadratic invariants and Leibniz rule"
Pissondes, J.C., 1999, J. Phys. A: Math. Gen. 32, 2871 (PDF)
"Quadratic relativistic invariant and metric form in quantum mechanics"
Jumarie, G., 2001, Int. J. Mod. Phys. A 16, 5061
"Schrödinger equation for quantum fractal space-time"
Back to presentation page
Laurent Nottale, (Hachette Littératures, 1998, collection Sciences),
319 pp.