Article PDF
Avoid common mistakes on your manuscript.
References
[A] Ahlfors, L.: Lectures on Quasiconformal Mappings. Princeton, N.J. Van Nostrand, 1966
[AB] Ahlfors, L., Bers, L.: The Riemann Mappings Theorem for Variable Metrics. Ann. Math., II. Ser.72-2, 385–404 (1960)
[Ash] Ashley, J.: Marker Automorphisms of the One-Sided Shift. Ergodic Theory Dyn. Syst.10, 247–262 (1990)
[BFK] Boyle, M., Franks, J., Kitchens, B.: Automorphisms of the One-Sided Shift and Subshifts of Finite Type. Ergodic Theory Dyn. Syst.10, 421–449 (1990)
[B1] Blanchard, P.: Complex Analytic Dynamics on the Riemann Sphere. Bull. Am. Math. Soc., New Ser.11, No. 1, 85–141 (1984)
[B2] Blanchard, P.: Disconnected Julia Sets. In: Chaotic Dynamics and Fractals, Ed. M. Barnsley, S. Demko, Academic Press, (1986), pp. 181–201
[BH1] Branner, B., Hubbard, J.: The Iteration of Cubic Polynomials I: The Global Topology of Parameter Space. Acta Math.160, 143–206 (1988)
[BH2] Branner, B., Hubbard, J.: The Iteration of Cubic Polynomials II. Patterns and Parapatterns. Acta Math (to appear)
[Br] Brolin, H.: Invariant Sets under Iteration of Rational Functions. Ark. Mat.6, 103–144 (1965)
[D] Devaney, R.L.: An Introduction to Chaotic Dynamical Systems, second edition. Redwood City, Calif.: Addison-Wesley Co. 1987
[DH1] Douady, A., Hubbard, J.: Itération des Polynômes quadratiques complexes. C.R. Acad. Sci., Paris, Ser. I29, 123–126 (1982)
[DH2] Douady, A., Hubbard, J.: Étude Dynamique des Polynôme Complexes. Publ. Math. Orsay. 84–102 (1984)
[DH3] Douady, A., Hubbard, J.: On the Dynamics of Polynomial-like Mappings. Ann. Sci. Ec. Norm. Super., IV. Ser.18, 287 (1985)
[F] Fatou, P.: Sur les Equations Fonctionelles, Bull. Soc. Math. Fr.47, 161–271 (1919)
[Fr] Franks, J.: Homology and Dynamical Systems. Conf. Board Math. Sci. Regional Conference Series.49 (1982)
[GK] Goldberg, L., Keen, L.: The Mapping Class Group of a Generic Quadratic Rational Map and Automorphisms of the Two Shift. Invent. Math.101, 335–372 (1990)
[H] Hedlund, G.: Endomorphisms and Automorphisms of the Shift Dynamical System. Math. Syst. Theory3, 320–375 (1969)
Julia, G.: Iteration des Applications Fonctionelles, J. Math. Pures Appl., 47–245 (1918)
[LV] Lehto, O., Virtannen, K.I., Quasi Conformal Mappings. Berlin Heidelberg New York: Springer 1965
[Ma] Mandelbrot, B.: The Fractal Geometry of Nature. San Francisco: Freeman and Co. 1982
[Mi] Milnor, J.: Remarks on Iterated Cubic Maps, SUNY Stony Brook 1990/6
[Mo] Morrey, C.B.: On the Solutions of Quasi-Linear Elliptic Partial Differential Equations. Trans. Am. Math. Soc.43, 126–166 (1938)
[S] Smale, S.: Diffeomorphisms with Many Periodic Points. In: Differential and Combinatorial Topology. (pp. 63–80) Princeton: Princeton University Press 1965
[Su] Sullivan, D.: Quasiconformal Maps and Dynamical Systems I, Solutions of the Fatou-Julia Problem on Wandering Domains. Ann. Math. II. Ser.122, 401–418 (1985)
[W] Wagoner, J.: Realizing Symmetries of a Shift. Ergodic Theory Dyn. Syst.8, 459–481 (1988)
Author information
Authors and Affiliations
Additional information
Oblatum 6-XII-1989 & 13-IX-1990
Research supported in part by the National Science Foundation grant #DMS 88-01277
Research supported in part by the National Science Foundation grants # DMS 870105 and # RII-8903049
Rights and permissions
About this article
Cite this article
Blanchard, P., Devaney, R.L. & Keen, L. The dynamics of complex polynomials and automorphisms of the shift. Invent. math. 104, 545–580 (1991). https://doi.org/10.1007/BF01245090
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01245090