A rigorous lower bound for the stability regions of the quadratic map

DOI10.1016/j.physd.2009.06.020zbMath1197.37060OpenAlexW2008232244MaRDI QIDQ732357

Warwick Tucker, Daniel Wilczak

Publication date: 9 October 2009

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2009.06.020

zbMATH Keywords

interval analysisperiodic orbitquadratic mapperiod-doubly bifurcation

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (10)

Rigorous Numerical Study of Low-Period Windows for the Quadratic Map ⋮ On parameter loci of the Hénon family ⋮ High-Order Parameterization of Stable/Unstable Manifolds for Long Periodic Orbits of Maps ⋮ Scaling and fine structure of superstable periodic orbits in the logistic map ⋮ Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps ⋮ Fractal sets attached to homogeneous quadratic maps in two variables ⋮ Rigorous numerics for critical orbits in the quadratic family ⋮ Systematic search for wide periodic windows and bounds for the set of regular parameters for the quadratic map ⋮ Cryptanalysis of a family of self-synchronizing chaotic stream ciphers ⋮ Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family

Cites Work

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• A computer-assisted proof of the Feigenbaum conjectures
• Simple mathematical models with very complicated dynamics

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