Fixed points of Feigenbaum's type for the equation \(f^ p(\lambda x)\equiv \lambda f(x)\)
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Publication:1058768
DOI10.1007/BF01212292zbMath0565.58031OpenAlexW1603798986MaRDI QIDQ1058768
Jean-Pierre Eckmann, Henri Epstein, Peter Wittwer
Publication date: 1984
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01212292
Fixed-point theorems (47H10) Iteration theory, iterative and composite equations (39B12) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Iteration of real functions in one variable (26A18)
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Metric universalities and systems of renormalization group equations for bimodal maps ⋮ Scaling symmetries in nonlinear dynamics. A view from parameter space ⋮ Binary tree approach to scaling in unimodal maps ⋮ Islands of stability and complex universality relations ⋮ On the hyperbolicity of Lorenz renormalization ⋮ Non-single-valley solutions for \(p\)-order Feigenbaum's type functional equation \(f(\varphi(x)) = \varphi^p(f(x))\) ⋮ Disorder versus order: global multifractal relationship between topological entropies and universal convergence rates. ⋮ Smooth solutions for the p-order functional equation f ( φ ( x ) ) = φ p ( f ( x ) ) ⋮ Similarity between the Mandelbrot set and Julia sets ⋮ Scaling of Mandelbrot sets generated by critical point preperiodicity
Cites Work
- Unnamed Item
- On iterations of \(1-\alpha x^2\) on \((-1,1)\)
- Universal properties of maps on an interval
- On the existence of Feigenbaum's fixed point
- Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
- Quantitative universality for a class of nonlinear transformations
- A computer-assisted proof of the Feigenbaum conjectures
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