References
- Falconer, K. J. (2004). Fractal Geometry: Mathematical Foundations and Applications. New Jersey: John Wiley & Sons.
- Kac, M. (1966). Can one hear the shape of a drum? Am. Math. Mon. 73(4P2): 1–23. DOI: 10.1080/00029890.1966.11970915
- Lapidus, M. L. (1991). Fractal drum, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture. Trans. Amer. Math. Soc. 325(2): 465–529. DOI: 10.1090/S0002-9947-1991-0994168-5
- Lapidus, M. L. (1992). Spectral and fractal geometry: From the Weyl-Berry conjecture for the vibrations of fractal drums to the Riemann Zeta-function. Math. Sci Eng. 186: 151–181.
- Lapidus, M. L. (1993). Vibrations of fractal drums, the Riemann hypothesis, waves in fractal media, and the Weyl-Berry conjecture. In: Ordinary and partial differential equations, Vol. IV, Proc. Twelth International Conference on “the Theory of Partial Differential Equations”, London: Longman Scientific and Technical, pp. 126–209.
- Lapidus, M. L., Neuberger, J. W., Renka, R. J, Griffith, C. A. (1996). Snowflake harmonis and computer graphics: numerical computation of spectra on fractal drums. Int. J. Bifurcation Chaos 6(7): 1185–1210. DOI: 10.1142/S0218127496000680
- Lapidus, M. L., Pang, M. (1995). Eigenfunctions of the Koch snowflake domain. Communmath. Phys. 172(2): 359–376. DOI: 10.1007/BF02099432
- Lapidus, M. L, Pearse, E. (2006). A tube formula for the Koch snowflake curve, with applications to complex dimensions. J. London Math. Soc. 74(2): 397–414. DOI: 10.1112/S0024610706022988
- Mauldin, R. D., Urbański, M. (2002). Fractal measures for parabolic IFS. Adv. Math. 168(2): 225–253. DOI: 10.1006/aima.2001.2049
- Neuberger, J. M., Sieben, N., Swift, J. W. (2006). Computing eigenfunctions on the Koch Snowflake: A new grid and symmetry. J. Comput. Appl. Math. 191(1): 126–142. DOI: 10.1016/j.cam.2005.03.075
- Pang, M. (1996). Approximation of ground state eigenfunction on the snowflake region. B Lond Math. Soc. 28(5): 488–494. DOI: 10.1112/blms/28.5.488
- Saupe, D. (1987). Efficient computation of Julia sets and their fractal dimension. Phys. D 28(3): 358–370. DOI: 10.1016/0167-2789(87)90024-8
- Strichartz, R. S., Wiese, S. C. Spectrum of the Laplacian on planar domains with fractal boundary (2020). http://pi.math.cornell.edu/s∼w972 (updated March 1).
- Yang, G. (2002). Some geometric properties of Julia sets and filled-in Julia sets of polynomials. Complex Var Theory Appl. 47(5): 383–391. DOI: 10.1080/02781070290013811