Scaling of Mandelbrot sets generated by critical point preperiodicity

DOI10.1007/BF01218762zbMath0587.30027OpenAlexW2047660337MaRDI QIDQ1072675

Henri Epstein, Jean-Pierre Eckmann

Publication date: 1985

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01218762

zbMATH Keywords

iterationscalingMandelbrot setrational maps

Mathematics Subject Classification ID

Topological dynamics (37B99) 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 (4)

Scaling symmetries in nonlinear dynamics. A view from parameter space ⋮ Parameter space of one-parameter complex mappings ⋮ Bifurcation rigidity ⋮ Similarity between the Mandelbrot set and Julia sets

Cites Work

• On the iteration of a rational function: Computer experiments with Newton's method
• Fixed points of Feigenbaum's type for the equation \(f^ p(\lambda x)\equiv \lambda f(x)\)
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