Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kiwi, Jan 2014. Puiseux series dynamics of quadratic rational maps. Israel Journal of Mathematics, Vol. 201, Issue. 2, p. 631.

    Bullett, Shaun and Sentenac, Pierrette 1994. Ordered orbits of the shift, square roots, and the devil's staircase. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 115, Issue. 03, p. 451.

  • Ergodic Theory and Dynamical Systems, Volume 12, Issue 3
  • September 1992, pp. 401-423

Bifurcations of dynamic rays in complex polynomials of degree two

  • Pau Atela (a1)
  • DOI:
  • Published online: 01 September 2008

In the study of bifurcations of the family of degree-two complex polynomials, attention has been given mainly to parameter values within the Mandelbrot set M (e.g., connectedness of the Julia set and period doubling). The reason for this is that outside M, the Julia set is at all times a hyperbolic Cantor set. In this paper weconsider precisely this, values of the parameter in the complement of M. We find bifurcations occurring not on the Julia set itself but on the dynamic rays landing on itfrom infinity. As the parameter crosses the external rays of M, in the dynamic plane the points of the Julia set gain and lose dynamic rays. We describe these bifurcations with the aid of a family of circle maps and we study in detail the case of the fixed points.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[B]P. Blanchard . Complex analytic dynamics on the Riemann sphere. Bull. Amer. Math. Soc. 11 (1984), 85141.

[Bo]P. Boyland . Bifurcations of circle Maps: Arnol'd tongues, bistability and rotation intervals. Commun. Math. Phys. 106 (1986), 353381.

[Dou]A. Douady . Algorithms for computing angles in the Mandelbrot set. Chaotic Dynamics and Fractals. M. Barnsley and S. G. Demko , eds, Academic Press: New York, 1986, 155168.

[He]M. Herman . Sur la conjugaison diffélrentiable des difieomorphismes du cercle à des rotations. Publ. Math., IHES 49 (1979), 5234.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *