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Laplacians on a family of quadratic Julia sets II
1. | Mathematics Department, Yale University, New Haven, CT 06510, United States |
2. | Mathematics Department, New York University, New York, NY 10012, United States |
3. | Mathematics Department, Malott Hall, Cornell Univeristy, Ithaca, NY 14853, United States |
References:
[1] |
S. Constantin, R. Strichartz and M. Wheeler, Analysis of the Laplacian and spectral operators on the Vicsek set, Comm. Pure Appl. Anal, 10 (2011), 1-44. |
[2] |
Stella C. Dong, Laplacians on a family of quadratic Julia sets II, http://www.math.cornell.edu/ cdong01/, March 2010. |
[3] |
A. Douady, Descriptions of compact sets in $\mathbb{C}$, in "Topological Methods in Modern Mathematics'' (eds. L. Goldberg and A. Phillips), Publish or Perish, Houston (1993), 429-465. |
[4] |
T. Flock and R. Strichartz, Laplacians on a family of Julia sets I, Trans. Amer. Math. Soc., to appear. |
[5] |
Jun Kigami, "Analysis on Fractals," volume 143 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 2001. |
[6] |
Jun Kigami and Michel L. Lapidus, Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals, Comm. Math. Phys., 158 (1993), 93-125. |
[7] |
J. Milnor, Periodic orbits, externals rays and the Mandelbrot set: an expository account, Geometrie Complexe et Systemes Dynamiques, 261 (2000), 277-333. |
[8] |
Luke G. Rogers and Alexander Teplyaev, Laplacians on the basilica Julia set, Comm. Pure Appl. Anal., 9 (2010), 211-231. |
[9] |
R. Strichartz, Fractals in the large, Can. J. Math., 50 (1998), 638-657. |
[10] |
Robert S. Strichartz, "Differential Equations on Fractals, A Tutorial,'' Princeton University Press, Princeton, NJ, 2006. |
[11] |
A. Teplyaev, Spectral analysis on infinite Sierpinski gaskets, J. Functional Anal., 159 (1998), 537-567. |
show all references
References:
[1] |
S. Constantin, R. Strichartz and M. Wheeler, Analysis of the Laplacian and spectral operators on the Vicsek set, Comm. Pure Appl. Anal, 10 (2011), 1-44. |
[2] |
Stella C. Dong, Laplacians on a family of quadratic Julia sets II, http://www.math.cornell.edu/ cdong01/, March 2010. |
[3] |
A. Douady, Descriptions of compact sets in $\mathbb{C}$, in "Topological Methods in Modern Mathematics'' (eds. L. Goldberg and A. Phillips), Publish or Perish, Houston (1993), 429-465. |
[4] |
T. Flock and R. Strichartz, Laplacians on a family of Julia sets I, Trans. Amer. Math. Soc., to appear. |
[5] |
Jun Kigami, "Analysis on Fractals," volume 143 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 2001. |
[6] |
Jun Kigami and Michel L. Lapidus, Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals, Comm. Math. Phys., 158 (1993), 93-125. |
[7] |
J. Milnor, Periodic orbits, externals rays and the Mandelbrot set: an expository account, Geometrie Complexe et Systemes Dynamiques, 261 (2000), 277-333. |
[8] |
Luke G. Rogers and Alexander Teplyaev, Laplacians on the basilica Julia set, Comm. Pure Appl. Anal., 9 (2010), 211-231. |
[9] |
R. Strichartz, Fractals in the large, Can. J. Math., 50 (1998), 638-657. |
[10] |
Robert S. Strichartz, "Differential Equations on Fractals, A Tutorial,'' Princeton University Press, Princeton, NJ, 2006. |
[11] |
A. Teplyaev, Spectral analysis on infinite Sierpinski gaskets, J. Functional Anal., 159 (1998), 537-567. |
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