no. 5
Existence and uniqueness of diffusions on finitely ramified self-similar fractals
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 30 (1997) no. 5, pp. 605-673. 
@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://www.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://www.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://www.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, Série 4, Tome 30 (1997) no. 5, pp. 605-673. doi : 10.1016/s0012-9593(97)89934-x. http://www.numdam.org/articles/10.1016/s0012-9593(97)89934-x/

[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 | Zbl

[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 | Zbl

[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 | Zbl

[4] C. M. Dafermos and M. Slemrod, Asymptotic behaviour of non-linear contraction semigroups (J. Functional Analysis, Vol. 13, 1973, pp. 97-106). | MR | Zbl

[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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[11] J. E. Hutchinson, Fractals and self-similarity (Indiana Univ. Math. J., Vol. 30, 1981, pp. 713-747). | MR | Zbl

[12] J. Kigami, Harmonic calculus on p.c.f. self-similar sets, (Trans. Am. Math. Soc., Vol. 335, 1993, pp. 721-755). | MR | Zbl

[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 | Zbl

[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). | MR | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[19] T. Lindstrøm, Brownian motion on nested fractals (Mem. Amer. Math. Soc., Vol. 420, 1990). | Zbl

[20] V. Metz, How many diffusions exist on the Viscek snowflake (Acta Applicandae Mathematicae, Vol. 32, 1993, pp. 227-241). | MR | Zbl

[21] V. Metz, Hilbert's Projective metric on cones of Dirichlet forms (Journal of Functional Analysis, Vol. 127, No 2, 1995). | MR | Zbl

[22] Moran, Additive functions of intervals and Haussdorf measure (Math. Proc., Cambridge Philos. Soc., Vol. 42, 1946, pp. 15-23). | MR | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

Cité par Sources :