Bifurcations of dynamic rays in complex polynomials of degree two

DOI10.1017/S0143385700006854zbMath0768.58034OpenAlexW2120277882MaRDI QIDQ4015515

P. Atela

Publication date: 18 January 1993

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700006854

zbMATH Keywords

bifurcationJulia setMandelbrot setdynamic raydegree-two complex quadratic polynomials

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

Fixed points of polynomial maps. Part II. Fixed point portraits ⋮ Dynamics of quadratic polynomials. I, II ⋮ Ordered orbits of the shift, square roots, and the devil's staircase ⋮ Puiseux series dynamics of quadratic rational maps ⋮ \(Se^x\): dynamics, topology, and bifurcations of complex exponentials ⋮ Extensions of homeomorphisms between limbs of the Mandelbrot set ⋮ Wandering orbit portraits ⋮ Homeomorphisms between limbs of the Mandelbrot set ⋮ Mating Siegel quadratic polynomials

Cites Work

• Bifurcations of circle maps: Arnol'd tongues, bistability and rotation intervals
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Complex analytic dynamics on the Riemann sphere