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Resources, Readings, and References

Resources, Readings, and References#

Textbook#

The course will make regular reference to [].

References#

[ASS86]

G. Albinet, G. Searby, and D. Stauffer. Fire propagation in a 2-D random medium. Journal de Physique, 47(1):1–7, 1986. URL: http://dx.doi.org/10.1051/jphys:019860047010100, doi:10.1051/jphys:019860047010100.

[BDM+88]

Michael F. Barnsley, Robert L. Devaney, Benoit B. Mandelbrot, Heinz-Otto Peitgen, Dietmar Saupe, and Richard F. Voss. The Science of Fractal Images. Springer-Verlag, 1 edition, 1988. ISBN 978-1-4612-8349-2. doi:10.1007/978-1-4612-3784-6.

[Bar06]

Michael Fielding Barnsley. SuperFractals. Cambridge University Press, September 2006. ISBN 9781107590168. URL: http://dx.doi.org/10.1017/CBO9781107590168, doi:10.1017/cbo9781107590168.

[Bur85]

William L. Burke. Applied differential geometry. Cambridge University Press, 1985. ISBN 0-521-26929-6. doi:10.1017/CBO9781139171786.

[Fal14]

Kenneth Falconer. Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons Inc., Hoboken, 3 edition, 2014. ISBN 978-1-119-94239-9.

[Fei78]

Mitchell J. Feigenbaum. Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics, 19(1):25–52, July 1978. URL: https://doi.org/10.1007%2Fbf01020332, doi:10.1007/bf01020332.

[GF95]

Dante Giarrusso and Yuval Fisher. A parameterization of the period $3$ hyperbolic components of the mandelbrot set. Proc. Am. Math. Soc., 123(12):3731–3731, December 1995. URL: http://dx.doi.org/10.1090/S0002-9939-1995-1301497-3, doi:10.1090/s0002-9939-1995-1301497-3.

[Mat95]

Pertti Mattila. Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability. Volume 44 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, April 1995. ISBN 9780511623813. doi:10.1017/cbo9780511623813.

[ML03]

Cleve Moler and Charles Van Loan. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1):3–49, 2003. URL: http://dx.doi.org/10.1137/S00361445024180, doi:10.1137/S00361445024180.

[NS89]

M. Nauenberg and H. J. Schellnhuber. Analytic evaluation of the multifractal properties of a newtonian julia set. Phys. Rev. Lett., 62(16):1807–1810, April 1989. URL: http://dx.doi.org/10.1103/PhysRevLett.62.1807, doi:10.1103/physrevlett.62.1807.

[PJurgensS04]

Heinz-Otto Peitgen, Hartmut Jürgens, and Dietmar Saupe. Chaos and Fractals: New Frontiers of Science. Springer New York, 2 edition, 2004. ISBN 0387202293. URL: http://dx.doi.org/10.1007/b97624, doi:10.1007/b97624.

[PTVF07]

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, third edition, 2007. URL: http://numerical.recipes.

[Sau87]

Dietmar Saupe. Efficient computation of Julia sets and their fractal dimension. Physica D: Nonlinear Phenomena, 28(3):358–370, October 1987. URL: http://dx.doi.org/10.1016/0167-2789(87)90024-8, doi:10.1016/0167-2789(87)90024-8.

[Sch91]

Manfred R. Schroeder. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. W. H. Freeman and Company, 1991. ISBN 9780486472041. URL: https://store.doverpublications.com/0486472043.html.

[SA94]

Dietrich Stauffer and Ammon Aharony. Introduction To Percolation Theory. Taylor & Francis, 2 edition, December 1994. ISBN 0748400273. URL: http://dx.doi.org/10.1201/9781315274386, doi:10.1201/9781315274386.

Linear Algebra#

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