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Original Articles

Critical Points of the Multiplier Map for the Quadratic Family

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References

  • [Buff and Gauthier 15] X. Buff and T. Gauthier. “Quadratic Polynomials, Multipliers and Equidistribution.” Proc. Amer. Math. Soc. 143:7 (2015), 3011–3017.
  • [Epstein] A. Epstein. Transversality in holomorphic dynamics. http://homepages.warwick.ac.uk/mases/Transversality.pdf.
  • [Firsova and Gorbovickis 19] T. Firsova and I. Gorbovickis. “Equidistribution of Critical Points of the Multipliers in the Quadratic Family.” arXiv:1903.00062, 2019.
  • [Giusti and Yakoubsohn 13] M. Giusti and J.-C. Yakoubsohn. “Multiplicity Hunting and Approximating Multiple Roots of Polynomial Systems.” In Recent Advances in Real Complexity and Computation, edited by José Luis Montaña and Luis M. Pardo, Volume 604 of Contemporary Mathematics, pp. 105–128. Providence, RI: American Mathematical Society, 2013.
  • [Gorbovickis 16] I. Gorbovickis. “Algebraic Independence of Multipliers of Periodic Orbits in the Space of Polynomial Maps of One Variable.” Ergod. Theory Dyn. Syst. 36:4 (2016), 1156–1166.
  • [Hubbard et al. 01] J. Hubbard, D. Schleicher, and S. Sutherland. “How to Find All Roots of Complex Polynomials by Newton’s Method.” Invent. Math. 146:1 (2001), 1–33.
  • [Hamal Hubbard 06] J. Hamal Hubbard. Teichmüller Theory and Applications to Geometry, Topology, and Dynamics. Vol. 1. Matrix editions, Ithaca, NY, 2006. Teichmüller theory, With contributions by Adrien Douady, William Dunbar, Roland Roeder, Sylvain Bonnot, David Brown, Allen Hatcher, Chris Hruska and Sudeb Mitra, With forewords by William Thurston and Clifford Earle.
  • [Levin 89] G. M. Levin. “On the Theory of Iterations of Polynomial Families in the Complex Plane.” Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 51 (1989), 94–106.
  • [Levin 09] G. Levin. “Multipliers of Periodic Orbits of Quadratic Polynomials and the Parameter Plane.” Isr. J. Math. 170:1 (2009), 285–315.
  • [Levin 11] G. Levin. “Rigidity and Non-local Connectivity of Julia Sets of Some Quadratic Polynomials.” Commun. Math. Phys. 304:2 (2011), 295–328.
  • [Milnor 93] J. Milnor. “Geometry and Dynamics of Quadratic Rational Maps.” Exp. Math. 2:1 (1993), 37–83 (With an appendix by the author and Lei Tan).
  • [Milnor 00] J. Milnor. “Periodic Orbits, Externals Rays and the Mandelbrot Set: An Expository Account.” Astérisque. 261:xiii (2000), 277–333 (Géométrie complexe et systèmes dynamiques (Orsay, 1995)).
  • [Milnor 06] J. Milnor. Dynamics in One Complex Variable, Volume 160 of Annals of Mathematics Studies, third edition. Princeton, NJ: Princeton University Press, 2006.
  • [Milnor 12] J. Milnor. “Hyperbolic components.” In Conformal Dynamics and Hyperbolic Geometry, edited by Francis Bonahon, Robert L. Devaney, Frederick P. Gardiner and Dragomir Šarić, Volume 573 of Contemporary Mathematics. pp. 183–232. Providence, RI: American Mathematical Society, 2012 (With an appendix by A. Poirier).

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