Self-Similarity for the Tricorn

References

• [Arai 16] Z. Arai. “On Loops in the Hyperbolic Locus of the Complex Hénon Map and their Monodromies.” Phys. D 334 (2016), 133–140.
   Web of Science ®Google Scholar
• [BBM 15] A. Bonifant, X. Buff, and J. Milnor. “Antipode Preserving Cubic Maps: The Fjord Theorem.” Available online (https://arxiv.org/abs/1512.01850/), 2015. arXiv:1512.01850.
   Google Scholar
• [CHRSC 89] W. D. Crowe, R. Hasson, P. J. Rippon, and P. E. D. Strain-Clark. “On the Structure of the Mandelbar Set.” Nonlinearity 2:4 (1989), 541–553.
   Web of Science ®Google Scholar
• [DH 85] A. Douady and J. H. Hubbard. “On the Dynamics of Polynomial-Like Mappings.” Ann. Sci. École Norm. Sup. (4) 18:2 (1985), 287–343.
   Web of Science ®Google Scholar
• [Ebe 99] D. Eberlein. “Rational Parameter Rays of Multibrot Sets.” Diploma diss., Zentrum Mathematik, Technische Universität München, 1999.
   Google Scholar
• [GS 97] J. Graczyk and G. Światek. “Generic Hyperbolicity in the Logistic Family.” Ann. Math. (2) 146:1 (1997), 1–52.
   Web of Science ®Google Scholar
• [Haï 00] P. Haïssinsky. “Modulation dans l’ensemble de Mandelbrot.” In The Mandelbrot Set, Theme and Variations (London Mathematical Society Lecture Note Series 274), edited by T. Lei, pp. 37–65. Cambridge: Cambridge Univ. Press, 2000.
   Google Scholar
• [Hru 06] S. L. Hruska. “A Numerical Method for Constructing the Hyperbolic Structure of Complex Hénon Mappings.” Found. Comput. Math. 6:4 (2006), 427–455.
   Web of Science ®Google Scholar
• [HS 14] J. Hubbard and D. Schleicher. “Multicorns are not Path Connected.” In Frontiers in Complex Dynamics: In Celebration of John Milnor’s 80th birthday, edited by A. Bonifant, M. Lyubich, & S. Sutherland, pp. 73–102. Princeton: Princeton University Press, 2014.
   Google Scholar
• [IK 12] H. Inou and J. Kiwi. “Combinatorics and Topology of Straightening Maps, I: Compactness and Bijectivity.” Adv. Math. 231:5 (2012), 2666–2733.
   Web of Science ®Google Scholar
• [IM 15] H. Inou and S. Mukherjee. Discontinuity of Straightening in Antiholomorphic Dynamics. Manuscript, 2015.
   Google Scholar
• [IM 16] H. Inou and S. Mukherjee. “Non-Landing Parameter Rays of the Multicorns.” Invent. Math. 204:3 (2016), 869–893.
   Web of Science ®Google Scholar
• [Ino 09] H. Inou. “Combinatorics and Topology of Straightening Maps II: Discontinuity.” Available online (https://arxiv.org/abs/0903.4289/), 2009. arXiv:0903.4289.
   Google Scholar
• [IS 08] H. Inou and M. Shishikura. The Renormalization for Parabolic Fixed Points and Their Perturbation. Preprint available from (https://www.math.kyoto-u.ac.jp/~mitsu/pararenorm/), 2008.
   Google Scholar
• [Kiw 01] J. Kiwi. “Rational Laminations of Complex Polynomials.” In Laminations and Foliations in Dynamics, Geometry and Topology, pp. 111–154, New York: Stony Brook, 2001.
   Google Scholar
• [Lyu 97] M. Lyubich. “Dynamics of Quadratic Polynomials. I, II.” Acta Math. 178:2 (1997), 185–247, 247–297.
   Web of Science ®Google Scholar
• [Mil 92] J. Milnor. “Remarks on Iterated Cubic Maps.” Experiment. Math. 1:1 (1992), 5–24.
   Google Scholar
• [MNS 17] S. Mukherjee, S. Nakane, and D. Schleicher. “On Multicorns and Unicorns II: Bifurcations in Spaces of Antiholomorphic Polynomials.” Ergodic Theory Dynam. Systems 37 (2017), 859–899. arXiv:1404.5031.
   Web of Science ®Google Scholar
• [Nak 93] S. Nakane. “Connectedness of the Tricorn.” Ergodic Theory Dynam. Systems 13:2 (1993), 349–356.
   Google Scholar
• [NS 03] S. Nakane and D. Schleicher. “On Multicorns and Unicorns. I. Antiholomorphic Dynamics, Hyperbolic Components and Real Cubic Polynomials.” Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13:10 (2003), 2825–2844.
   Web of Science ®Google Scholar
• [NS 96] S. Nakane and D. Schleicher. “The Nonarcwise-Connectedness of the Tricorn.” Sūrikaisekikenkyūsho Kōkyūroku 959 (1996), 73–83. Problems concerning complex dynamical systems (Japanese) (Kyoto, 1995).
   Google Scholar
• [PR 08] C. L. Petersen and P. Roesch. “The Yoccoz Combinatorial Analytic Invariant.” In Holomorphic Dynamics and Renormalization, edited by M. Lyubich and M. Yampolsky, pp. 145–176. Providence: American Mathematical Society, 2008.
   Google Scholar
• [Sch XX] D. Schleicher. “On Fibers and Local Connectivity of Mandelbrot and Multibrot Sets.” Preprint available from (https://arxiv.org/abs/math/9902155). arXiv:math/9902155.
   Google Scholar