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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

[1] M. T. BARLOW, Random walks, electrical resistance, and nested fractals (Asymptotic Problems in Probability Theory : Stochastic models and diffusions on fractals, Montreal : Longman, 1993, pp. 131-157).  MR 96i:60082 |  Zbl 0791.60097
[2] M. T. BARLOW and R. F. BASS, Construction of the Brownian motion on the Sierpinski carpet, (Ann. Inst. Henri Poincaré, Vol. 25, 1989, pp. 225-257).
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, 1988, pp. 543-623).  MR 89g:60241 |  Zbl 0635.60090
[4] C. M. DAFERMOS and M. SLEMROD, Asymptotic behaviour of non-linear contraction semigroups (J. Functional Analysis, Vol. 13, 1973, pp. 97-106).  MR 49 #11336 |  Zbl 0267.34062
[5] P. G. DOYLE and J. L. SNELL. Randon walks and electrical networks (Math. Assoc. Amer., 1984).
[6] FALCONER, Fractal Geometry : Mathematical Foundations and Applications, Wiley, Chichester, 1990.  Zbl 0689.28003
[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, 1994).  MR 96f:60126 |  Zbl 0838.31001
[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, 1993, pp. 151-161).  MR 94d:60129 |  Zbl 0764.60081
[9] S. GOLDSTEIN, Random walks and diffusions on fractals, in : IMA Math Appl., Vol. 8 (H. Kesten, ed.), Springer-Verlag, New York, 1987, pp. 121-129).  MR 88g:60245 |  Zbl 0621.60073
[10] K. HATTORI, T. HATTORI, H. WATANABE, Gaussian field theories on general networks and the spectral dimensions (Progress of Theoritical Physics, Supplement No 92, 1987).  MR 89k:81118
[11] J. E. HUTCHINSON, Fractals and self-similarity (Indiana Univ. Math. J., Vol. 30, 1981, pp. 713-747).  MR 82h:49026 |  Zbl 0598.28011
[12] J. KIGAMI, Harmonic calculus on p.c.f. self-similar sets, (Trans. Am. Math. Soc., Vol. 335, 1993, pp. 721-755).  MR 93d:39008 |  Zbl 0773.31009
[13] J. KIGAMI, Harmonic calculus on limits of networks and its application to dendrites (Journal of Functional Analysis, Vol. 128, No. 1, February 15, 1995).  MR 96e:60130 |  Zbl 0820.60060
[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, 1993, pp. 765-786).
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, 1987, pp. 251-274).  MR 89e:60149 |  Zbl 0645.60081
[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, 1994 i, pp. 137-195).  MR 96g:58196 |  Zbl 0836.35108
[18] Y. LE JAN, Mesures associées à une forme de Dirichlet. Applications (Bull. Soc. Math. de France, Vol. 106, 1978, pp. 61-112).
Numdam |  MR 81c:31014 |  Zbl 0393.31008
[19] T. LINDSTRØM, Brownian motion on nested fractals (Mem. Amer. Math. Soc., Vol. 420, 1990).  Zbl 0688.60065
[20] V. METZ, How many diffusions exist on the Viscek snowflake (Acta Applicandae Mathematicae, Vol. 32, 1993, pp. 227-241).  MR 94m:31010 |  Zbl 0795.31011
[21] V. METZ, Hilbert's Projective metric on cones of Dirichlet forms (Journal of Functional Analysis, Vol. 127, No 2, 1995).  MR 96c:31009 |  Zbl 0831.47047
[22] MORAN, Additive functions of intervals and Haussdorf measure (Math. Proc., Cambridge Philos. Soc., Vol. 42, 1946, pp. 15-23).  MR 7,278f |  Zbl 0063.04088
[23] R.D. NUSSBAUM, Hilbert's Projective Metric and Iterated Nonlinear Maps (Mem. Am. Math. Soc., Vol. 75, No 391, Amer. Math. Soc. Providence, 1988).  MR 89m:47046 |  Zbl 0666.47028
[24] S. ROEHRIG and R. SINE, The structure of w-limit sets of non-expansive maps (Proc. Amer. Math. Soc., Vol. 81, 1981, pp. 398-400).  MR 82f:47068 |  Zbl 0474.47033
[25] C. SABOT, Diffusions sur les espaces fractals (Thèse de l'université Pierre et Marie Curie, 1995).
[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, 1995).  MR 96i:60085 |  Zbl 0848.60076
[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, 1916, pp. 629-632).  JFM 46.0295.02
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