Bounds on the unstable eigenvalue for period doubling

DOI10.1007/BF02108789zbMath0704.58040OpenAlexW1983870485MaRDI QIDQ917124

Henri Epstein, Jean-Pierre Eckmann

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1007/bf02108789

zbMATH Keywords

boundsperiod-doublingunimodal mapsunstable eigenvalue

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Low-dimensional dynamical systems (37E99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (10)

Feigenbaum Numbers for Certain Flat-Top Families ⋮ A new type of period-doubling scaling behavior in two-dimensional area-preserving map ⋮ Symbolic dynamics behind the singular continuous power spectra of continuous flows ⋮ A note on the Artuso-Aurell-Cvitanovic approach to the Feigenbaum tangent operator ⋮ Asymptotics of scaling parameters for period-doubling in unimodal maps with asymmetric critical points ⋮ Bounds on the unstable eigenvalue for the asymmetric renormalization operator for period doubling ⋮ Multiparameter critical situations, universality and scaling in two-dimensional period-doubling maps ⋮ Analytic Solutions of the Cvitanović–Feigenbaum and Feigenbaum–Kadanoff–Shenker Equations ⋮ Physical meaning for Mandelbrot and Julia sets ⋮ Quadratic convergence in period doubling to chaos for trapezoid maps

Cites Work

• Unnamed Item
• Computer methods and Borel summability applied to Feigenbaum's equation
• New proofs of the existence of the Feigenbaum functions
• Universal properties of maps on an interval
• On the existence of Feigenbaum's fixed point
• A complete proof of the Feigenbaum conjectures
• Quantitative universality for a class of nonlinear transformations
• Fixed points of composition operators. II

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