Systematic search for wide periodic windows and bounds for the set of regular parameters for the quadratic map

DOI10.1063/1.4983172zbMath1387.37036OpenAlexW2613236685WikidataQ47818750 ScholiaQ47818750MaRDI QIDQ4642594

Zbigniew Galias

Publication date: 23 May 2018

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4983172

zbMATH Keywords

periodic windowquadratic map

Mathematics Subject Classification ID

Iteration of real functions in one variable (26A18) Dynamical systems involving maps of the interval (37E05)

Related Items (5)

Mode selection and stability of attractors in Chua circuit driven by piezoelectric sources ⋮ Scaling and fine structure of superstable periodic orbits in the logistic map ⋮ Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps ⋮ Rigorous numerics for critical orbits in the quadratic family ⋮ On the validity of linear response theory in high-dimensional deterministic dynamical systems

Uses Software

• MPFR
• CAPD

Cites Work

• Unnamed Item
• Unnamed Item
• A rigorous lower bound for the stability regions of the quadratic map
• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• The universal metric properties of nonlinear transformations
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• Almost every real quadratic map is either regular or stochastic.
• Proving the existence of long periodic orbits in 1D maps using interval Newton method and backward shooting
• On finite limit sets for transformations on the unit interval
• Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family
• The Topology of Chaos
• Computable conditions for the occurrence of non-uniform hyperbolicity in families of one-dimensional maps
• Rigorous Numerical Study of Low-Period Windows for the Quadratic Map
• Quantitative hyperbolicity estimates in one-dimensional dynamics
• A Precise Calculation of the Feigenbaum Constants
• Simple mathematical models with very complicated dynamics
• Chaos

This page was built for publication: Systematic search for wide periodic windows and bounds for the set of regular parameters for the quadratic map