Existence of the Siegel disc renormalization fixed point
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Publication:4299204
DOI10.1088/0951-7715/7/3/011zbMath0803.47056OpenAlexW2090058052MaRDI QIDQ4299204
Publication date: 3 January 1995
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0951-7715/7/3/011
computer-assisted proofrescaling factorcommuting fixed pointexistence of the critical fixed point of Siegel's disc renormalization operatorWidom's operator
Fixed-point theorems (47H10) Interval and finite arithmetic (65G30) Stability theory for smooth dynamical systems (37C75) Periodic and quasi-periodic flows and diffeomorphisms (37C55)
Related Items (9)
Existence of the FS-type renormalisation fixed point for unidirectionally-coupled pairs of maps ⋮ Combination laws for scaling exponents and relation to the geometry of renormalization operators ⋮ The Boundaries of Golden-Mean Siegel Disks in the Complex Quadratic Hénon Family Are Not Smooth ⋮ Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters ⋮ Unnamed Item ⋮ Renormalization and Siegel disks for complex Hénon maps ⋮ Renormalization in the golden-mean semi-Siegel Hénon family: universality and non-rigidity ⋮ Boundaries of Siegel disks: Numerical studies of their dynamics and regularity ⋮ Rigorous computer-assisted bounds on the period doubling renormalization fixed point and eigenfunctions in maps with critical point of degree 4
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