@article{ASENS_1997_4_30_5_605_0, author = {Sabot, C.}, title = {Existence and uniqueness of diffusions on finitely ramified self-similar fractals}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {605--673}, publisher = {Elsevier}, volume = {Ser. 4, 30}, number = {5}, year = {1997}, doi = {10.1016/s0012-9593(97)89934-x}, mrnumber = {98h:60118}, zbl = {0924.60064}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/s0012-9593(97)89934-x/} }
TY - JOUR AU - Sabot, C. TI - Existence and uniqueness of diffusions on finitely ramified self-similar fractals JO - Annales scientifiques de l'École Normale Supérieure PY - 1997 SP - 605 EP - 673 VL - 30 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/s0012-9593(97)89934-x/ DO - 10.1016/s0012-9593(97)89934-x LA - en ID - ASENS_1997_4_30_5_605_0 ER -
%0 Journal Article %A Sabot, C. %T Existence and uniqueness of diffusions on finitely ramified self-similar fractals %J Annales scientifiques de l'École Normale Supérieure %D 1997 %P 605-673 %V 30 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/s0012-9593(97)89934-x/ %R 10.1016/s0012-9593(97)89934-x %G en %F ASENS_1997_4_30_5_605_0
Sabot, C. Existence and uniqueness of diffusions on finitely ramified self-similar fractals. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 30 (1997) no. 5, pp. 605-673. doi : 10.1016/s0012-9593(97)89934-x. http://archive.numdam.org/articles/10.1016/s0012-9593(97)89934-x/
[1] 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 | Zbl
,[2] Construction of the Brownian motion on the Sierpinski carpet, (Ann. Inst. Henri Poincaré, Vol. 25, 1989, pp. 225-257). | Numdam | MR | Zbl
and ,[3] Brownian motion on the Sierpinski gasket (Prob. Th. Rel. Fields, Vol. 79, 1988, pp. 543-623). | MR | Zbl
and ,[4] Asymptotic behaviour of non-linear contraction semigroups (J. Functional Analysis, Vol. 13, 1973, pp. 97-106). | MR | Zbl
and ,[5] Randon walks and electrical networks (Math. Assoc. Amer., 1984).
and .[6] Fractal Geometry : Mathematical Foundations and Applications, Wiley, Chichester, 1990. | Zbl
,[7] Dirichlet forms and symetric Markov processes (de Gruyter Stud. Math., Vol. 19, Walter de Gruyter, Berlin, New-York, 1994). | MR | Zbl
, and ,[8] 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 | Zbl
,[9] Random walks and diffusions on fractals, in : IMA Math Appl., Vol. 8 (H. Kesten, ed.), Springer-Verlag, New York, 1987, pp. 121-129). | MR | Zbl
,[10] Gaussian field theories on general networks and the spectral dimensions (Progress of Theoritical Physics, Supplement No 92, 1987). | MR
, , ,[11] Fractals and self-similarity (Indiana Univ. Math. J., Vol. 30, 1981, pp. 713-747). | MR | Zbl
,[12] Harmonic calculus on p.c.f. self-similar sets, (Trans. Am. Math. Soc., Vol. 335, 1993, pp. 721-755). | MR | Zbl
,[13] Harmonic calculus on limits of networks and its application to dendrites (Journal of Functional Analysis, Vol. 128, No. 1, February 15, 1995). | MR | Zbl
,[14] 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). | MR | Zbl
,[15] 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 | Zbl
,[16] Lecture on diffusion processes on nested fractals, Springer Lecture Notes in Math.
,[17] 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 | Zbl
,[18] Mesures associées à une forme de Dirichlet. Applications (Bull. Soc. Math. de France, Vol. 106, 1978, pp. 61-112). | Numdam | MR | Zbl
,[19] Brownian motion on nested fractals (Mem. Amer. Math. Soc., Vol. 420, 1990). | Zbl
,[20] How many diffusions exist on the Viscek snowflake (Acta Applicandae Mathematicae, Vol. 32, 1993, pp. 227-241). | MR | Zbl
,[21] Hilbert's Projective metric on cones of Dirichlet forms (Journal of Functional Analysis, Vol. 127, No 2, 1995). | MR | Zbl
,[22] Additive functions of intervals and Haussdorf measure (Math. Proc., Cambridge Philos. Soc., Vol. 42, 1946, pp. 15-23). | MR | Zbl
,[23] Hilbert's Projective Metric and Iterated Nonlinear Maps (Mem. Am. Math. Soc., Vol. 75, No 391, Amer. Math. Soc. Providence, 1988). | MR | Zbl
,[24] The structure of w-limit sets of non-expansive maps (Proc. Amer. Math. Soc., Vol. 81, 1981, pp. 398-400). | MR | Zbl
and ,[25] Diffusions sur les espaces fractals (Thèse de l'université Pierre et Marie Curie, 1995).
,[26] Existence et unicité de la diffusion sur un espace fractal (C. R. Acad. Sci. Paris, T. 321, Séries I, pp. 1053-1059, 1995). | MR | Zbl
,[27] Espaces de Dirichlet reliés par des points. Application au calcul de l'opérateur de renormalisation sur les fractals finiment ramifiés, Preprint.
,[28] 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
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