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Table of contents for this issue | Previous article | Next article Sabot, C. Existence and uniqueness of diffusions on finitely ramified self-similar fractals. Annales scientifiques de l'École Normale Supérieure, Sér. 4, 30 no. 5 (1997), p. 605-673 Full text djvu | pdf | Reviews MR 98h:60118 | Zbl 0924.60064 | 2 citations in Numdam stable URL: http://www.numdam.org/item?id=ASENS_1997_4_30_5_605_0 Bibliography [2] M. T. BARLOW and R. F. BASS, Construction of the Brownian motion on the Sierpinski carpet, (Ann. Inst. Henri Poincaré, Vol. 25, Numdam | MR 91d:60183 | Zbl 0691.60070 [3] M. T. BARLOW and E. A. PERKINS, Brownian motion on the Sierpinski gasket (Prob. Th. Rel. Fields, Vol. 79, [4] C. M. DAFERMOS and M. SLEMROD, Asymptotic behaviour of non-linear contraction semigroups (J. Functional Analysis, Vol. 13, [5] P. G. DOYLE and J. L. SNELL. Randon walks and electrical networks (Math. Assoc. Amer., [6] FALCONER, Fractal Geometry : Mathematical Foundations and Applications, Wiley, Chichester, [7] M. FUKUSHIMA, Y. OSHIMA and M. TAKEDA, Dirichlet forms and symetric Markov processes (de Gruyter Stud. Math., Vol. 19, Walter de Gruyter, Berlin, New-York, [8] M. FUKUSHIMA, Dirichlet forms, diffusion processes and spectral dimensions for nested fractals, in : Ideas and Methods in Mathematical analysis, Stochastics and Applications (Proc. Conf. in Memory of Hoegh-Krohn, Vol. 1 (S. Albevario et al., eds.), Cambridge Univ. Press, Cambridge, [9] S. GOLDSTEIN, Random walks and diffusions on fractals, in : IMA Math Appl., Vol. 8 (H. Kesten, ed.), Springer-Verlag, New York, [10] K. HATTORI, T. HATTORI, H. WATANABE, Gaussian field theories on general networks and the spectral dimensions (Progress of Theoritical Physics, Supplement No 92, [11] J. E. HUTCHINSON, Fractals and self-similarity (Indiana Univ. Math. J., Vol. 30, [12] J. KIGAMI, Harmonic calculus on p.c.f. self-similar sets, (Trans. Am. Math. Soc., Vol. 335, [13] J. KIGAMI, Harmonic calculus on limits of networks and its application to dendrites (Journal of Functional Analysis, Vol. 128, No. 1, February 15, [14] T. KUMAGAI, Regularity, closedness, and spectral dimension of the Dirichlet forms on p.c.f. self-similar sets (J. Math. Kyoto Univ., Vol. 33, Article | MR 94i:28006 | Zbl 0798.58042 [15] S. KUSUOKA, A diffusion process on a fractal, in : (Probabilistic Methods in Mathematical Physics (Proc. of Taniguchi Intern. Symp. (K. Ito and N. Ikeda, eds.) Kinokuniya, Tokyo, [16] S. KUSUOKA, Lecture on diffusion processes on nested fractals, Springer Lecture Notes in Math. [17] M. L. LAPIDUS, Analysis on fractals, Laplacians on self-similar sets, non-commutative geometry and spectral dimensions (Topological Methods in Nonlinear Analysis, Vol. 4, No 1, [18] Y. LE JAN, Mesures associées à une forme de Dirichlet. Applications (Bull. Soc. Math. de France, Vol. 106, Numdam | MR 81c:31014 | Zbl 0393.31008 [19] T. LINDSTRØM, Brownian motion on nested fractals (Mem. Amer. Math. Soc., Vol. 420, [20] V. METZ, How many diffusions exist on the Viscek snowflake (Acta Applicandae Mathematicae, Vol. 32, [21] V. METZ, Hilbert's Projective metric on cones of Dirichlet forms (Journal of Functional Analysis, Vol. 127, No 2, [22] MORAN, Additive functions of intervals and Haussdorf measure (Math. Proc., Cambridge Philos. Soc., Vol. 42, [23] R.D. NUSSBAUM, Hilbert's Projective Metric and Iterated Nonlinear Maps (Mem. Am. Math. Soc., Vol. 75, No 391, Amer. Math. Soc. Providence, [24] S. ROEHRIG and R. SINE, The structure of w-limit sets of non-expansive maps (Proc. Amer. Math. Soc., Vol. 81, [25] C. SABOT, Diffusions sur les espaces fractals (Thèse de l'université Pierre et Marie Curie, [26] C. SABOT, Existence et unicité de la diffusion sur un espace fractal (C. R. Acad. Sci. Paris, T. 321, Séries I, pp. 1053-1059, [27] C. SABOT, Espaces de Dirichlet reliés par des points. Application au calcul de l'opérateur de renormalisation sur les fractals finiment ramifiés, Preprint. [28] W. SIERPINSKI, Sur une courbe Cantorienne qui contient une image biunivoque et continue de toute courbe donnée (C. R. Acad. Sci. Paris, T. 162, |
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